All Questions
Tagged with mathematics geometry
613
questions
9
votes
2
answers
1k
views
Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?
Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?
No two rectangles can be the same size.
- 12.7k
2
votes
0
answers
192
views
Ernie and the conduits of constant cross-section
It all started last week, when Acme Engineering loaned him a prototype version of their 3D Home Printer (this was as a reward for Ernie providing them, patent-free, with a suitable building material - ...
- 14k
27
votes
5
answers
4k
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Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?
Can you tile a $25 \times 25$ square (no overlaps, no gaps) with a mixture of $2 \times 2$ squares and $3 \times 3$ squares?
This puzzle is by David A. Klarner.
Clarification: The number of $2 \times ...
- 12.7k
3
votes
1
answer
336
views
Build a slanted pyramid with ten L-shaped blocks
Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces:
Use 10 of the above L-shaped pieces to make the following shape:
- 12.7k
11
votes
4
answers
1k
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Make a square table top with the minimal needed amount of straight cuts
inspired by : Make a square table top with six (or fewer) pieces
A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
- 9,308
10
votes
2
answers
509
views
Make a square table top with six (or fewer) pieces
A man had three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square respectively. He wanted to cut these into the fewest pieces possible that would fit together and form a ...
- 12.7k
6
votes
5
answers
694
views
Circles crossing every cell of an NxN grid
What is the least number of circles you need to draw, such that every cell of an NxN grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
- 36.3k
1
vote
1
answer
183
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Recursive rhombic dodecahedron tiling
Say you have a single rhombic dodecahedron, call it "layer p0". If you then tile identical dodecahedrons around it so that it gets completely covered, the number of dodecahedrons on the ...
2
votes
1
answer
538
views
Is it possible to fill an arbitrarily large hex grid completely given these rules? #2
Based off of this.
Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be ...
- 3,185
4
votes
1
answer
517
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Is it possible to fill an arbitrarily large hex grid completely given these rules?
Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be filled or empty.
A ...
13
votes
3
answers
2k
views
Circles crossing every cell of an 8x8 grid
What is the least number of circles you need to draw, such that every cell of an 8x8 grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
- 36.3k
6
votes
1
answer
294
views
April Fools Origami Update
Me (Sunny Lu) and Ωmega_3301 have made a special April Fools edition of origami puzzles.
The objective is to fold a shape into a rectangle with uniform thickness. The thickness will be given to you.
...
- 3,185
7
votes
1
answer
544
views
origami WAVE t2
Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The grey part is not included in the puzzle; the purple part is the puzzle.
Although solutions are not required ...
- 3,185
-4
votes
1
answer
151
views
Logic and Geometry Problem #6
Is it possible for a deadlock to occur in Necklace? Can there be a square on which neither Red nor Blue can place a stone?
If it is possible, I need to see an example of that.
If a deadlock is not ...
- 335
4
votes
1
answer
178
views
origami USHAPE t3
Fold the shape into a rectangle such that the rectangle is 3 layers thick everywhere.
Although solutions are not required to be applicable in real life, using an actual sheet of paper is a great ...
- 3,185