Questions tagged [packing]
A puzzle that involves arranging objects optimally in order to fit in a specified space.
88 questions
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Tilted packing: fit 7 identical polyominoes into an 8.5×8.5 square
You are given 7 identical copies of the following polyomino (made of unit squares):
Goal is to place all 7 pieces inside a square tray of side length:
8.5 units
You may rotate by any angle and flip ...
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Is it possible to pack an 11x11x11 cube using copies of the two given shapes?
Is it possible to pack (no overlaps, no gaps) an 11x11x11 cube using copies of the two shapes shown below?
Text description of the two objects in the above image:
Object 1: Middle layer has 5 unit ...
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The slanted blocks box problem
Woody Woodcutter is preparing his special slanted wooden blocks box. His nephew likes to put slanted roofs on every construction, so he made a special box with many slanted blocks to add to his ...
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Compact arrangement of Qwirkle tiles
Qwirkle tiles are identically-sized squares. Each has two attributes: one of 6 symbols and one of 6 colors. There are 3 tiles for each combination of symbol and color, thus 6×6×3 = 108 tiles. We want ...
- 537
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You mean, I can't just put my space-filling curve anywhere I want??
In the making of this puzzle, I had to generate every possible space-filling curve for both the 5x8 grid and the 5x9 grid.
The 5x8 grid went as expected. No matter where my space-filling curve ...
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Double double coil trouble
If you find it tedious and annoying to coil up a garden hose after use, well, you've come to the right place.
Here's a nice quotation taken from a poem by Amy Woolard:
...
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Minimize number of tiles to make hexagon packing stuck
The question Maximize the number of triangular tiles that can fit inside a hexagon after three tiles are placed shows a tiling puzzle where you have 18 triangles with angles of (30,120,30) that need ...
- 2,419
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Maximize the number of triangular tiles that can fit inside a hexagon after three tiles are placed
While traveling in Europe recently, I bought a tiling puzzle for my daughter. (It is a Grimm’s wooden puzzle, exactly like the one in this link.) The puzzle contains 18 congruent tiles, each of which ...
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3D Packing Puzzle: Can 17 Mixed-Size Blocks Fill a Cube?
You are given a cube-shaped box with dimensions 5×5×5. Your task is to determine whether the following blocks can be arranged to fit perfectly inside the box without any gaps or overlaps:
5 blocks of ...
- 377
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Packing coins in a square frame
Show that there exists a square frame and a set of identical circular coins, such that the coins can be rigidly packed in the frame in more than one arrangement.
Remarks:
"Rigidly packed" ...
- 6,136
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Can the circles fit inside the triangle?
The diagram shows an equilateral triangle, a green semicircle and two congruent red circles. Wherever things look tangent, they are tangent.
Can two more red circles fit inside the triangle (with no ...
- 6,136
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Packing cubes into spheres
Packing problems are well known, often hard and sometimes fun. If we want to pack unit squares into a circle then this beautiful page shows some solutions. One interesting feature is shown first in ...
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Fitting 10 pieces of pizza in a box
Inspired by Fitting the 9th piece into the pizza box
2 pizzas with radius r are each cut into 8 identical slices. 6 pieces were eaten so there are 10 pieces left. ...
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Fitting the 9th piece into the pizza box
I bought two pizzas that were radially sliced into 8 identical pieces each. I ate 7 of the 16 pieces. Now to save space I want to place the remaining 9 pieces into one box without cutting them and ...
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How many of the tetracubes can be used to make a 2x4x4 cuboid?
Beginner puzzle
This puzzle is intended to be suitable for people who are new to puzzle solving.
Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle.
...