question
listlengths 1
1
| answer
dict |
|---|---|
[
{
"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"
}
|
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