136
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Prove that π > 3
I didn't have a knife with me, so I only used my unit circle cookie cutter to split each square like this:
I then rearranged the parts into this shape:
Since the angle covered by this shape is ...
- 78.6k
107
votes
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67
votes
44
votes
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Dissecting the exotic bulbfish
Cut along the red lines and move the pieces as indicated by the yellow arrows.
As is usual with this kind of dissection, it helps if you look at the area to work out the length of the side of the ...
- 55k
39
votes
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7x10 floor and a 8x8 and a 6x1 carpet, only one cut allowed
Here is one way it can be done.
Path of discovery:
- 16.7k
38
votes
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Pythagorean quilts
The optimal solution is
which is achievable (for example) like this:
For another (or perhaps, the other) way to achieve the minimal number of pieces, you can check out OP's self-answer below.
Here'...
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33
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Pythagorean pentagons
6 pieces, no flipping required:
History:
7 pieces, no flipping required:
8 pieces, requires two flips
9 pieces, requires one flip
very similar:
10 pieces, no flipping required
not very elegant, ...
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32
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Pythagorean pentagons
My efforts to minimize the number of pieces did not improve upon loopy walt's best, but here is another 7-piece solution without flipping:
Sixteen pieces, with some flipping required.
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28
votes
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Maximum Pieces of Cake in Four Cuts
If all cuts are straight cuts and the cake is a rectangular prism or cylinder, it's not possible. From Wikipedia's page on the Cake Number:
In mathematics, the cake number, denoted by Cn, is the ...
- 17.5k
27
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Dissecting the holey octomino into a square
Well, from my viewpoint this is a four-piece dissection, since parts of each piece don't move relatively to each other. They are even connected, to some extent. However, I would completely agree that ...
- 6,962
26
votes
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25
votes
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A pizza dilemma
I found a solution where every slice is strictly larger than 8 square inches:
I found a solution, and after comparing it to @spherical-wug-in-a-vacuum's solution, I found a solution which uses fewer, ...
- 7,260
25
votes
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Dividing shape into 2 congruent pieces
One solution that follows the grid lines:
Alternative representation (for browsers/fonts that don't display Unicode U+1F7E5 or U+1F7E6 correctly):
- 371
24
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Pythagorean pentagons
OK, I'll give you my solution for reference.
And just for fun, here is another seven piece solution.
And finally my own 6-piece solution
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23
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Four fanatics and one checkerboard
I'm not sure why you'd need ANY sort of dissection for this.
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22
votes
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Cutting a cross made of 5 equal squares by 2 straight cut into 4 figure to together form a square
Here is a good way of seeing how this dissection comes about.
- 55k
21
votes
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Can I Haz My Eye Center'd?
One (non-straight) cut:
(Or a different image by Carl Löndahl: https://nup.pw/YK9cjY.png)
21
votes
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Near-fill with 3x1 long triominos, how to do a different void square than the center square?
The trick to this puzzle is to:
(And here are those tilings: the center was already given, and the rest are obtainable from these by rotation.)
- 150k
21
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Cut this shape into 3 pieces and fit them together to form a square
Here is a solution that works in the general case of two squares of any size placed next to each other.
- 55k
20
votes
20
votes
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Restore the square
Apologies for the crude drawing but I think you need to do something like this
Some deduction that went into this answer
- 138k
19
votes
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Obtain four equal parts with a single cut
Okay, I don't know how people here create images that fast, but I get a more sheet-like solution.
- 2,053
19
votes
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Piece of Cake for King Solomon
To divide the cake into n equal pieces,
Proof:
Here is a drawing to illustrate how it works:
- 55k
19
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Cut this shape into 3 pieces and fit them together to form a square
A slightly different graphic:
- 62.2k
19
votes
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17
votes
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Dissecting the holey octomino into a square
I seriously doubt that this can be done in 4 pieces or less. It would be a miracle if it was possible, but it obviously isn't a walk in the park to prove. Regardless, to get people started, I have ...
- 9,917
17
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How can the white cross be cut into 5 smaller pieces that can be resembled into the two smaller red crosses shown?
Here is a visual answer.
And the pieces joined together
- 10.3k
17
votes
Accepted
Dividing a square field into 5 equal regions
Edit/Note: I gave this answer assuming fractional fences where not allowed.
As such I did not carefully think about the second picture.
Obviously that answer is not optimal if fractional fence ...
- 9,411
16
votes
Pythagorean quilts
Just for reference here is my intended answer.
I thought it is so weird it would take you days to crack. As it happens you didn't have to, you came up with a simpler and even more logical solution.
...
- 31k
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