Dataset Viewer
question
listlengths 1
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|---|---|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨ ▢▢▨\n▢▨▨ ▢▢▢\n▢▨▨ ▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▢ ▨▢▢\n▨▨▨ ▢▢▢\n▨▢▢ ▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▢ ▨▢▢\n▨▢▢ ▨▨▢\n▢▢▢ ▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨ ▢▢▢\n▨▨▨ ▢▢▢\n▢▢▨ ▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢ ▨▨▢\n▢▨▢ ▨▢▨\n▨▨▨ ▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢ ▨▨▨\n▢▢▢ ▨▨▢\n▨▢▨ ▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢ ▨▢▢\n▢▨▢ ▨▢▨\n▨▢▢ ▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨ ▢▨▢\n▢▢▨ ▢▨▨\n▢▨▨ ▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨ ▢▨▨\n▢▨▢ ▨▢▢\n▢▨▨ ▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨ ▢▢▢\n▨▨▨ ▢▢▢\n▢▨▢ ▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨ ▢▢▢\n▢▢▨ ▢▨▢\n▨▨▢ ▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨ ▢▨▢\n▢▢▨ ▢▨▢\n▢▨▢ ▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▢ ▨▢▢\n▢▢▨ ▢▢▨\n▨▢▨ ▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢ ▨▨▨\n▨▢▨ ▢▢▢\n▢▢▢ ▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨ ▢▨▢\n▢▢▨ ▢▢▨\n▨▨▨ ▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢ ▨▢▢\n▢▨▢ ▨▢▨\n▢▨▢ ▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨ ▢▨▢\n▨▢▢ ▨▨▢\n▨▢▢ ▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨ ▢▢▢\n▨▢▨ ▢▨▢\n▢▢▢ ▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢ ▨▨▨\n▨▨▢ ▢▢▢\n▨▢▢ ▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨ ▢▢▢\n▨▨▢ ▨▢▢\n▢▨▨ ▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢ ▢▨▨▨\n▢▨▢▢ ▨▨▢▨\n▨▢▢▨ ▢▨▨▢\n▢▢▢▨ ▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▨ ▢▢▨▢\n▨▨▢▨ ▢▨▢▢\n▢▨▢▢ ▨▨▢▨\n▨▨▨▢ ▨▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▨ ▢▨▢▨\n▨▨▨▢ ▨▢▢▢\n▢▨▢▨ ▢▨▢▨\n▢▨▢▨ ▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢ ▢▢▨▨\n▨▨▨▢ ▨▢▢▢\n▨▨▨▢ ▨▢▢▢\n▨▨▢▢ ▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▢ ▨▢▢▢\n▢▢▢▨ ▢▨▨▨\n▨▨▢▨ ▢▨▢▢\n▢▢▢▢ ▨▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▨ ▢▢▢▨\n▢▢▢▨ ▢▨▨▨\n▨▨▢▨ ▢▢▢▢\n▢▢▢▨ ▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢ ▨▨▨▨\n▨▨▢▢ ▢▨▢▢\n▨▨▨▢ ▨▢▢▢\n▨▨▢▢ ▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▢ ▢▨▢▨\n▨▨▢▢ ▨▨▢▢\n▢▨▢▨ ▢▨▢▨\n▢▨▨▨ ▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢ ▨▨▢▢\n▢▢▢▨ ▢▨▨▨\n▨▢▨▨ ▢▢▨▢\n▢▨▢▨ ▢▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▨ ▢▨▢▢\n▢▢▨▢ ▨▢▨▨\n▢▨▨▨ ▢▢▢▨\n▢▢▨▨ ▢▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▨ ▢▢▨▢\n▨▢▢▢ ▢▨▨▢\n▢▨▨▨ ▢▢▢▨\n▢▨▨▨ ▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▢ ▨▢▢▢\n▢▢▨▢ ▢▢▨▨\n▨▢▢▨ ▢▨▨▢\n▨▨▢▢ ▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢ ▨▢▢▨\n▢▨▢▢ ▨▨▢▨\n▨▢▨▢ ▨▢▨▢\n▨▢▢▨ ▢▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▨ ▢▢▨▨\n▢▨▨▨ ▢▢▢▨\n▨▢▢▢ ▨▨▢▢\n▢▢▨▨ ▢▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢ ▨▨▨▨\n▨▨▢▢ ▨▢▢▢\n▢▢▨▨ ▢▢▨▨\n▢▨▢▢ ▨▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▨ ▢▨▨▨\n▨▨▢▢ ▨▨▢▢\n▢▨▨▢ ▨▢▢▨\n▨▢▨▨ ▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢ ▨▢▨▨\n▢▨▨▨ ▢▢▢▨\n▨▢▨▢ ▨▢▢▢\n▨▨▨▨ ▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▢ ▨▢▢▢\n▢▨▨▨ ▢▢▢▨\n▢▨▢▢ ▨▨▢▨\n▨▨▨▨ ▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▢▨ ▢▨▢▢\n▨▨▨▨ ▢▢▢▢\n▢▢▨▨ ▢▢▨▨\n▢▢▢▢ ▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▨ ▢▢▨▨\n▨▢▨▢ ▨▢▨▢\n▨▨▢▨ ▢▢▢▢\n▨▨▨▢ ▨▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▨▢ ▨▢▢▢▨\n▢▢▨▢▢ ▨▨▢▨▨\n▢▢▨▨▢ ▨▢▢▨▨\n▨▢▢▨▨ ▢▢▨▢▢\n▢▨▢▨▨ ▢▢▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢▨ ▢▨▨▨▨\n▢▨▨▢▨ ▢▨▢▢▨\n▢▨▨▢▢ ▢▨▢▢▨\n▨▨▨▢▢ ▨▨▢▢▢\n▢▨▢▢▢ ▨▨▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢▨ ▢▨▨▨▢\n▨▢▢▨▨ ▢▢▨▨▢\n▢▨▢▢▨ ▢▨▢▢▨\n▨▨▨▢▨ ▢▨▢▢▢\n▢▢▢▢▢ ▨▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▢▢ ▨▨▢▨▢\n▢▨▨▢▢ ▨▨▢▢▨\n▢▨▢▨▢ ▨▢▨▢▨\n▨▨▨▨▨ ▢▢▢▢▢\n▢▢▢▨▢ ▢▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▨▨ ▢▢▨▢▨\n▨▢▢▢▨ ▢▨▢▨▢\n▨▨▨▢▢ ▨▨▢▢▢\n▢▢▨▨▢ ▨▢▢▨▨\n▨▢▢▢▨ ▢▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▢▨ ▢▨▨▢▨\n▢▢▢▨▢ ▨▢▨▨▢\n▨▢▢▢▨ ▢▨▨▨▢\n▢▢▨▨▨ ▢▢▢▨▨\n▨▨▢▢▨ ▢▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢▨ ▢▨▨▨▢\n▨▨▨▢▢ ▨▨▢▢▢\n▢▢▨▨▢ ▨▢▢▨▨\n▢▨▢▢▢ ▨▢▨▢▨\n▢▨▨▨▢ ▨▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▨▨ ▢▢▢▨▢\n▨▢▢▨▨ ▢▢▨▨▢\n▨▨▨▨▢ ▨▢▢▢▢\n▨▨▢▨▢ ▨▢▢▢▢\n▨▨▢▨▢ ▨▢▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢▢ ▨▨▨▨▨\n▨▨▢▢▨ ▢▨▨▢▢\n▢▨▢▢▨ ▢▨▨▢▨\n▨▨▢▢▨ ▢▨▨▢▢\n▨▢▢▢▨ ▢▢▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢▨ ▢▨▨▨▨\n▢▨▨▨▨ ▢▢▢▢▨\n▨▨▨▨▢ ▨▢▢▢▢\n▢▢▢▨▢ ▢▢▨▨▨\n▢▢▢▨▢ ▨▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢▨ ▢▨▢▨▨\n▨▨▨▢▨ ▢▨▢▢▢\n▢▨▨▢▢ ▨▨▢▢▢\n▨▢▢▨▨ ▢▢▨▨▢\n▢▢▢▢▢ ▨▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢▨ ▢▨▨▨▢\n▨▢▨▢▢ ▨▨▢▨▢\n▢▨▢▢▢ ▨▨▨▢▢\n▨▢▢▨▢ ▨▢▨▨▢\n▢▢▢▨▢ ▨▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▨▢ ▨▢▢▨▨\n▢▨▨▢▢ ▨▨▢▢▨\n▨▨▢▨▨ ▢▢▨▢▢\n▨▢▢▨▢ ▢▢▨▨▢\n▨▨▨▨▢ ▨▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▢▨▢ ▨▢▨▢▢\n▨▨▨▨▨ ▢▢▢▢▢\n▢▨▨▢▨ ▢▨▢▢▨\n▨▨▨▢▨ ▢▨▢▢▢\n▢▢▨▨▨ ▢▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢▨ ▢▨▢▨▨\n▨▢▨▨▨ ▢▢▢▨▢\n▢▢▢▢▨ ▢▨▨▨▢\n▨▢▨▢▨ ▢▨▢▨▢\n▨▢▨▨▢ ▨▢▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▢ ▨▢▢▢▢\n▢▨▢▨▢ ▨▢▨▢▨\n▢▢▨▢▨ ▢▢▢▨▨\n▢▨▢▢▨ ▢▨▨▢▨\n▢▢▢▢▨ ▢▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢▨ ▢▨▢▨▨\n▢▢▨▢▨ ▢▨▢▨▨\n▢▢▢▢▢ ▨▢▨▨▨\n▨▢▢▨▨ ▢▢▨▨▢\n▢▢▨▨▢ ▨▢▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▨▢ ▨▢▨▨▢\n▨▨▢▨▢ ▨▢▢▢▢\n▢▨▨▢▢ ▨▨▢▢▨\n▢▨▢▨▢ ▨▢▨▢▨\n▢▨▨▢▢ ▨▨▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢▨ ▢▨▢▨▨\n▢▢▨▨▢ ▨▢▢▨▨\n▢▨▢▨▢ ▨▢▨▢▨\n▨▢▢▢▢ ▨▨▢▨▢\n▨▢▢▢▨ ▢▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▨▢ ▨▢▨▨▨\n▨▢▢▢▨ ▢▨▨▨▢\n▢▨▨▢▨ ▢▨▢▢▨\n▢▢▢▢▢ ▨▨▨▨▨\n▨▢▨▨▢ ▢▢▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▨▢▨ ▢▨▢▢▨▨\n▢▢▨▨▨▢ ▨▢▢▢▢▨\n▨▢▨▢▢▨ ▢▨▨▢▨▢\n▨▢▢▨▨▢ ▨▢▢▨▨▢\n▨▨▢▨▨▢ ▨▢▢▨▢▢\n▨▢▢▨▨▢ ▨▢▢▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 5)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▨▨ ▢▢▢▢▢▢\n▢▢▨▢▨▢ ▨▢▨▢▨▨\n▨▢▢▢▨▨ ▢▢▨▨▨▢\n▢▨▨▨▨▨ ▢▢▢▢▢▨\n▨▢▨▢▢▢ ▨▨▢▢▨▢\n▢▢▨▨▢▨ ▢▨▢▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▢▢▢ ▨▨▢▢▢▨\n▨▢▢▢▢▨ ▢▨▨▨▨▢\n▨▨▨▢▨▢ ▨▢▨▢▢▢\n▨▢▢▨▨▨ ▢▢▢▨▨▢\n▢▢▨▨▢▨ ▢▨▢▢▨▨\n▨▨▨▨▢▢ ▨▨▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 6)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▢▢▢ ▨▨▨▢▨▢\n▢▢▢▨▢▨ ▢▨▢▨▨▨\n▨▨▢▨▢▢ ▨▨▢▨▢▢\n▢▢▨▢▨▨ ▢▢▢▢▨▨\n▢▢▢▨▢▨ ▢▨▢▨▨▨\n▨▢▨▨▢▨ ▢▨▢▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▨▢▨ ▢▨▢▢▢▢\n▨▢▢▢▨▢ ▨▢▨▨▨▢\n▢▢▨▢▨▨ ▢▢▨▢▨▨\n▢▢▢▨▨▨ ▢▢▢▨▨▨\n▢▨▨▨▢▨ ▢▨▢▢▢▨\n▨▨▢▨▨▢ ▨▢▢▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 6)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▨▢▨ ▢▨▢▢▢▨\n▨▨▢▢▨▨ ▢▢▨▨▢▢\n▢▢▢▨▨▢ ▨▢▢▨▨▨\n▢▨▨▨▢▨ ▢▢▢▢▢▨\n▨▢▨▢▨▨ ▢▢▨▢▨▢\n▢▢▢▢▢▢ ▨▨▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▢▢▨ ▢▨▨▨▢▨\n▢▨▢▨▢▨ ▢▨▢▨▢▨\n▢▨▨▢▢▨ ▢▨▨▢▢▨\n▨▨▢▢▢▢ ▨▨▨▨▢▢\n▨▢▢▢▨▨ ▢▢▨▨▨▢\n▨▢▢▢▨▢ ▢▢▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▨▨▢ ▨▢▢▨▨▨\n▢▢▨▨▨▨ ▢▢▢▢▨▨\n▢▢▢▢▨▢ ▨▢▨▨▨▨\n▨▨▢▢▢▨ ▢▨▨▨▢▢\n▢▨▢▨▨▨ ▢▢▢▨▢▨\n▨▨▢▨▢▨ ▢▢▢▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▢▢▢ ▨▨▨▢▨▢\n▨▢▢▢▢▢ ▨▨▨▨▨▢\n▢▢▨▢▢▨ ▢▨▨▢▨▨\n▢▢▢▢▢▨ ▢▨▨▨▨▨\n▨▢▨▨▢▢ ▨▢▢▢▨▢\n▢▢▢▢▨▢ ▨▢▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▨▨▢ ▨▢▢▢▨▢\n▨▨▢▨▢▢ ▨▨▢▨▢▢\n▨▢▨▨▢▢ ▨▨▢▢▨▢\n▢▨▨▨▢▨ ▢▨▢▢▢▨\n▢▨▨▢▢▨ ▢▨▨▢▢▨\n▢▨▢▢▢▨ ▢▢▨▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▨▨ ▢▢▢▢▢▢\n▨▨▨▨▢▨ ▢▨▢▢▢▢\n▢▢▢▢▢▢ ▨▨▨▨▨▨\n▢▨▨▢▨▨ ▢▢▨▢▢▨\n▨▨▢▢▢▢ ▨▨▨▨▢▢\n▢▨▢▨▢▢ ▨▨▢▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▢▨▨ ▢▢▨▨▢▨\n▢▨▢▢▨▢ ▨▢▨▨▢▨\n▢▢▢▨▨▢ ▨▢▢▨▨▢\n▨▢▢▨▢▨ ▢▨▢▨▨▢\n▨▨▢▢▢▨ ▢▨▨▨▢▢\n▨▢▢▢▢▢ ▨▨▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▢▢▢ ▨▨▨▢▢▢\n▨▨▨▢▢▨ ▢▨▨▢▢▢\n▢▨▨▢▨▢ ▨▢▨▢▢▨\n▨▢▢▢▢▨ ▢▨▨▨▢▢\n▢▨▢▢▢▨ ▢▨▨▨▢▨\n▨▨▢▢▢▢ ▨▨▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▢▢▨ ▢▨▨▢▢▢\n▢▢▢▨▢▨ ▢▨▢▨▨▨\n▨▨▨▨▨▢ ▨▢▢▢▢▢\n▢▨▨▢▢▨ ▢▢▨▢▢▨\n▢▢▨▢▢▢ ▨▨▨▢▨▨\n▨▢▢▨▨▢ ▨▢▢▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▢▢▨ ▢▨▨▢▨▢\n▢▨▢▢▢▨ ▢▨▨▨▢▨\n▢▢▢▨▨▨ ▢▢▢▨▨▢\n▨▨▢▢▢▨ ▢▨▨▨▢▢\n▨▨▢▨▢▢ ▨▨▢▨▢▢\n▢▢▢▢▢▢ ▨▨▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▢▢▨ ▢▨▨▢▢▢\n▢▢▢▨▨▨ ▢▢▢▨▨▢\n▢▢▢▨▨▢ ▨▢▢▨▨▨\n▨▨▨▨▨▢ ▨▢▢▢▢▢\n▨▢▨▢▢▨ ▢▨▨▢▨▢\n▨▢▢▢▨▢ ▨▢▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 5)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▢▨▢ ▨▢▨▨▢▨\n▨▨▨▢▨▨ ▢▢▨▢▢▢\n▨▢▨▢▢▢ ▨▨▨▢▨▢\n▢▢▨▨▨▢ ▨▢▢▢▢▨\n▨▢▨▢▢▨ ▢▨▨▢▨▢\n▢▢▢▢▢▢ ▨▨▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▢▨▨ ▢▢▨▢▨▢\n▨▢▨▢▨▢ ▨▢▨▢▨▢\n▨▨▨▢▨▢ ▨▢▨▢▢▢\n▢▨▢▢▢▨ ▢▨▨▨▢▨\n▢▢▢▨▨▨ ▢▢▢▨▨▢\n▨▢▨▢▨▢ ▨▢▨▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▨▢▨ ▢▨▢▨▨▨\n▨▢▢▨▨▢ ▨▢▢▨▨▢\n▢▢▨▢▨▨ ▢▢▨▢▨▨\n▨▢▢▨▢▢ ▨▨▢▨▨▢\n▨▨▢▢▨▨ ▢▢▨▨▢▢\n▨▢▢▢▢▢ ▨▨▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▢▨ ▢▨▢▢▢▢\n▨▨▢▢▢▢ ▨▨▨▨▢▢\n▢▨▢▢▨▨ ▢▢▨▨▢▨\n▢▨▢▨▢▨ ▢▨▢▨▢▨\n▨▢▢▢▢▢ ▨▨▢▨▨▢\n▢▨▨▢▢▨ ▢▨▨▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▨▨▨ ▢▢▢▢▢▢▢\n▨▨▨▢▨▢▢ ▨▨▢▨▢▢▢\n▢▢▨▨▨▢▢ ▨▨▢▢▢▨▨\n▨▢▨▢▨▢▢ ▨▨▢▨▢▨▢\n▨▢▢▨▢▢▢ ▨▨▨▢▨▨▢\n▨▢▢▢▨▢▢ ▨▨▢▢▨▨▢\n▨▨▢▢▢▢▢ ▨▨▨▨▨▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▨▢▨▢ ▨▢▨▢▨▨▨\n▢▢▢▢▨▨▢ ▨▢▢▨▨▨▢\n▨▨▢▢▨▨▢ ▨▢▢▨▨▢▢\n▢▨▢▢▢▢▢ ▨▨▨▨▨▢▨\n▢▢▨▢▢▢▢ ▨▨▨▨▢▨▨\n▢▢▢▨▢▢▢ ▨▨▨▢▨▨▨\n▨▢▢▢▢▢▨ ▢▨▨▨▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(7, 6)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▢▢▨▨▨ ▢▢▢▨▨▨▨\n▢▨▢▢▢▨▢ ▨▢▨▨▨▢▢\n▨▢▢▨▢▨▨ ▢▢▨▢▨▨▢\n▨▢▨▢▨▢▢ ▨▨▢▨▢▨▢\n▨▢▨▢▨▢▢ ▨▨▢▨▢▨▢\n▢▢▨▨▨▢▨ ▢▨▢▢▢▨▨\n▨▢▨▨▢▨▢ ▨▢▨▢▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(7, 6)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▢▢▨ ▢▨▨▢▢▢▢\n▢▢▢▢▨▢▢ ▨▨▢▨▨▨▨\n▨▢▨▨▢▢▢ ▨▨▨▢▢▨▢\n▢▨▨▨▢▨▨ ▢▢▨▢▢▢▨\n▨▨▢▨▨▢▨ ▢▨▢▢▨▢▢\n▨▨▢▢▨▢▢ ▢▨▢▨▨▢▢\n▢▨▨▨▢▢▨ ▢▨▨▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▨▨▢ ▨▢▢▢▢▢▢\n▢▢▢▨▢▨▢ ▨▢▨▢▨▨▨\n▨▢▢▢▢▢▨ ▢▨▨▨▢▨▢\n▨▨▢▨▢▨▢ ▨▢▨▢▨▢▢\n▢▢▢▨▨▨▨ ▢▢▢▢▨▨▨\n▢▨▢▢▢▨▨ ▢▢▨▨▨▢▨\n▨▢▨▢▢▢▨ ▢▨▨▨▢▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 5)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢▨▢▨ ▢▨▢▨▨▨▢\n▢▢▨▨▢▢▢ ▨▢▨▢▢▨▨\n▨▢▢▨▢▢▢ ▨▨▨▢▨▨▢\n▢▨▢▢▨▢▨ ▢▨▢▨▨▢▨\n▨▨▢▨▢▨▢ ▨▢▨▢▨▢▢\n▢▢▨▢▨▢▨ ▢▨▢▨▢▨▨\n▢▨▢▢▨▨▨ ▢▢▢▨▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(2, 6)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢▢▢▨ ▢▨▨▨▢▨▨\n▢▨▢▢▨▢▢ ▨▨▢▨▨▢▨\n▨▢▢▢▢▨▨ ▢▢▨▨▨▨▢\n▢▨▢▨▨▨▢ ▨▢▢▢▨▢▨\n▨▢▢▢▨▨▨ ▢▢▢▨▨▨▢\n▢▨▢▨▢▢▨ ▢▨▨▢▨▢▨\n▢▢▨▨▢▨▨ ▢▢▨▢▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▢▨▨▨ ▢▢▢▨▢▢▢\n▨▢▢▨▨▢▢ ▨▨▢▢▨▨▢\n▨▢▨▨▨▢▨ ▢▨▢▢▢▨▢\n▨▢▢▨▢▨▢ ▨▢▨▢▨▨▢\n▨▢▨▢▢▢▢ ▢▨▨▨▢▨▢\n▢▨▢▢▢▨▨ ▢▢▨▨▨▢▨\n▢▢▢▨▢▨▢ ▨▢▨▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▨▢▨▢ ▨▢▨▢▢▨▨\n▢▢▢▢▨▢▨ ▢▨▢▨▨▨▨\n▨▢▢▨▨▢▢ ▨▨▢▢▨▨▢\n▢▢▨▨▨▨▨ ▢▢▢▢▢▨▨\n▢▢▨▨▨▢▢ ▢▨▢▢▢▨▨\n▨▢▨▨▢▨▢ ▨▢▨▢▢▨▢\n▨▨▨▨▨▢▢ ▨▨▢▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▨▨▨▢▢ ▨▨▢▢▢▢▢\n▨▨▢▢▢▨▢ ▨▢▨▨▨▢▢\n▢▨▢▨▢▢▢ ▨▨▨▢▨▢▨\n▢▢▨▨▨▨▢ ▨▢▢▢▢▨▨\n▢▨▨▨▢▨▨ ▢▢▨▢▢▢▨\n▢▨▢▢▢▢▨ ▢▨▨▢▨▢▨\n▨▨▨▨▨▢▨ ▢▨▢▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢▢▨▢ ▨▢▢▨▨▨▢\n▨▨▨▢▨▨▨ ▢▢▢▨▢▢▢\n▨▨▨▢▢▨▢ ▨▢▨▨▢▢▢\n▢▨▨▢▢▢▨ ▢▨▨▨▢▢▨\n▢▢▢▨▨▢▢ ▨▨▢▢▨▨▨\n▢▢▢▨▨▢▨ ▢▨▢▢▨▨▨\n▨▨▨▨▢▢▢ ▨▨▨▢▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(3, 7)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▨▢▢▨ ▢▨▨▢▨▢▨\n▨▢▢▢▨▢▢ ▨▨▢▨▨▨▢\n▢▢▨▢▢▨▢ ▨▢▨▨▢▨▨\n▨▢▢▨▨▨▨ ▢▢▢▢▨▨▢\n▢▢▢▢▨▨▨ ▢▢▢▢▨▨▨\n▨▢▢▨▨▨▨ ▢▢▢▢▨▨▢\n▢▢▢▨▢▨▢ ▨▢▨▢▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▢▢▨▢ ▨▢▨▨▢▢▨\n▨▢▨▨▢▨▨ ▢▢▨▢▢▨▢\n▢▢▨▢▨▢▢ ▨▨▢▨▢▨▨\n▨▨▢▢▨▢▨ ▢▨▢▨▨▢▢\n▢▨▨▢▨▢▢ ▨▨▢▨▢▢▨\n▨▢▢▢▨▨▨ ▢▢▢▨▢▨▢\n▨▨▨▢▨▢▨ ▢▨▢▨▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▢▨▢▨▨▢ ▨▢▢▨▢▨▨\n▨▨▢▨▢▨▨ ▢▢▨▢▨▢▢\n▢▢▨▢▨▨▨ ▢▢▢▨▢▨▨\n▢▨▨▨▢▨▨ ▢▢▨▢▢▢▨\n▢▢▨▢▢▨▢ ▨▢▨▨▢▨▨\n▢▢▢▨▨▢▨ ▢▨▢▢▨▨▢\n▢▨▨▢▨▨▢ ▨▢▢▨▢▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(7, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▢▨▢▨ ▢▨▢▨▨▢▨\n▨▨▨▢▢▢▢ ▨▨▨▨▢▢▢\n▨▨▨▢▨▢▨ ▢▨▢▨▢▢▢\n▨▢▢▢▨▢▢ ▨▨▢▨▨▨▢\n▨▢▢▢▨▨▢ ▨▢▢▨▨▨▢\n▢▨▨▢▢▢▨ ▢▨▨▨▢▢▨\n▢▢▢▢▨▢▢ ▢▨▢▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(1, 1)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▢▢▨▨▨ ▢▢▢▨▨▨▢\n▢▨▨▢▨▨▢ ▨▢▢▨▢▢▨\n▢▢▢▨▢▨▨ ▢▢▨▢▨▨▨\n▨▨▨▨▨▢▨ ▢▨▢▢▢▢▢\n▨▢▢▢▢▢▨ ▢▨▨▨▨▨▢\n▢▢▢▢▢▨▢ ▨▢▨▨▨▢▨\n▢▢▢▢▨▨▨ ▢▢▢▨▨▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(6, 2)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▨▢▨▨▨▢ ▨▢▢▢▨▢▢\n▨▨▨▢▨▨▢ ▨▢▢▨▢▢▢\n▢▢▨▨▢▨▨ ▢▢▨▢▢▨▨\n▨▨▨▢▨▨▢ ▨▢▢▨▢▢▢\n▢▨▢▨▢▢▨ ▢▨▨▢▨▢▢\n▢▢▨▢▢▨▨ ▢▢▨▨▢▨▨\n▨▨▨▢▢▨▨ ▢▢▨▨▢▢▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(7, 3)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▨▢▨▨▢ ▨▢▢▨▢▢▨\n▨▨▢▨▢▢▨ ▢▨▨▢▨▢▢\n▨▢▢▨▨▢▨ ▢▨▢▢▨▨▢\n▢▢▢▢▢▨▨ ▢▢▨▨▢▨▨\n▢▢▨▨▨▢▨ ▢▨▢▢▢▨▨\n▨▨▨▢▨▨▨ ▢▢▢▨▢▢▢\n▢▨▢▨▢▢▨ ▢▨▨▢▨▢▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▨▢▨▢▢▨▢ ▨▢▨▨▢▨▢\n▨▨▢▢▨▨▢ ▨▢▢▨▨▢▢\n▨▨▨▢▢▢▨ ▢▨▨▨▢▢▢\n▨▢▢▢▢▨▨ ▢▢▨▢▨▨▢\n▢▢▢▨▨▢▢ ▨▨▢▢▨▨▨\n▨▨▢▨▨▢▢ ▨▨▢▢▨▢▢\n▢▢▨▨▢▨▨ ▢▢▨▢▢▨▨",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(4, 4)}"
],
"type": "contains_any"
}
|
[
{
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot in the suitcase.\nYou must always answer in the format \\boxed{(x, y)} using coordinates from the second half.\n\nThis is an example suitcase:\n▨▢▨ ▢▨▢\n▢▨▢ ▨▢▢\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase that has not been closed yet. You must give the coordinates of where to place the object on the second half of the suitcase. The bottom-left item is (1, 1).\nTo do this you must visualize the suitcase folding. This means that the first half will be flipped and placed on the second half. For the example above, this is how the suitcase will look when it is closed:\n\n▨▨▨\n▨▨▢\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 2)}\n\nThis is another example suitcase:\n▢▢▢ ▢▨▨\n▢▨▨ ▢▢▨\n▨▨▢ ▨▢▢\nThis suitcase is a 2x3 suitcase. Folding the left half onto the right gives:\n\n▢▨▨\n▨▨▨\n▨▨▨\n\nTherefore the answer to this suitcase is \\boxed{(3, 3)}\n\nNow find an empty slot in this suitcase:\n\n▢▨▢▨▨▢▢ ▨▨▢▢▨▢▨\n▢▢▢▢▨▢▢ ▨▨▢▨▨▨▨\n▢▢▨▢▢▨▨ ▢▢▨▨▢▨▨\n▢▢▢▢▨▢▨ ▢▨▢▨▨▨▨\n▢▨▨▢▨▢▢ ▨▨▢▨▢▢▨\n▢▨▢▨▨▨▨ ▢▢▢▢▢▢▨\n▨▢▢▨▢▨▢ ▨▢▨▢▨▨▢",
"role": "user"
}
] |
{
"contains_any": [
"\\boxed{(5, 2)}"
],
"type": "contains_any"
}
|
End of preview. Expand
in Data Studio
Dataset Card for PackBench 🧳
Dataset Summary
PackBench is a suite of visual-spatial reasoning tasks where language models are asked to "pack" items into virtual suitcases. Each suitcase is represented as a grid that folds in half, and models must determine the correct location to place a missing item based on a mirrored folding operation. The dataset is designed to evaluate LLMs' abilities in spatial reasoning, mirroring transformations, and structured decision-making.
PackBench is structured as a collection of multiple-choice or short-answer evaluation tasks with clear visual-textual instructions and examples. It is ideal for evaluating models that claim multi-step spatial inference capabilities.
Supported Tasks and Leaderboards
Task: visual spatial reasoning
Type: Evaluation / Benchmarks
Format: Prompt-based QA with grounded visual instructions (ASCII art).
Answer format: Coordinates in \boxed{(x, y)} format.
Evaluation Metric: Exact match with allowed correct boxed answers.
Languages
English (en)
Dataset Structure
Each example contains:
"question": A list of one user message with the prompt."answer": A dictionary with accepted answer(s) (usingcontains_anyfor flexibility).
Example Entry
{
"question": [
{
"role": "user",
"content": "You are an expert at packing suitcases.\nYou must place an item in an empty slot..."
}
],
"answer": {
"type": "contains_any",
"contains_any": ["\\boxed{(3, 2)}"]
}
}
Dataset Creation
The dataset was procedurally generated using a Python script. For each suitcase:
- The suitcase is defined as a 2D grid split into two halves.
- One cell in the folded final view is left empty.
- The folded state is decomposed into a plausible left and right half (non-overlapping).
- The model must reason about folding the left side over the right to determine where the empty cell is in the final folded suitcase.
This mirrors a cognitive visual-spatial task often found in human IQ or pattern reasoning tests.
Suitcase sizes range from 2x3 to 10x20 (i.e., up to 400 cells), testing both fine-grained spatial reasoning and scale handling.
Sizes
PackBench includes suitcases of varying complexity:
- Sizes: From
3x6up to20x40 - Number of examples per size:
20 - Total examples: 360
Intended Use
Use Cases
- Evaluate the spatial reasoning capabilities of large language models (LLMs).
- Benchmark models trained on visual or multimodal reasoning tasks.
- Include in broader diagnostic evaluation sets for LLM alignment, logical reasoning, and task generalization.
- Test raw reasoning especially at larger sizes (10x20+).
Limitations
- ASCII art may be misinterpreted by purely text-based models not trained for structured visual parsing.
- Assumes the model understands spatial mirroring and coordinate systems.
Citation
If you use PackBench in your research or applications, please cite it as:
@misc{packbench2025,
title={PackBench: A Spatial Reasoning Benchmark for Language Models},
year={2025},
author={{Deca AI}},
howpublished={\url{https://huggingface.co/datasets/deca-ai/packbench}},
}
License
CC BY 4.0
Tags
llm-evaluation · spatial-reasoning · benchmarks · folding · mirroring · suitcase · ASCII · reasoning · alignment
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