# Tag Info

Accepted

### How can this shape perfectly cover a cube?

The shape Using this, we can make a guess for how the cube might be folded: Once that fold is done, the shape looks more like this: A drawing of the finished product: And an animation of the whole ...
• 146k
Accepted

### Is this duplo train track under too much tension?

First, we can check that there is no angular misalignment. Since 12 curved pieces are needed to make a full circle, the number of left pieces minus the number of right pieces must be a multiple of 12. ...
• 18.9k
Accepted

### 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 ...
• 77.4k
Accepted

### Can you fold a square into a square of one-fifth the area?

The way to do this is:
• 146k
Accepted

### Can you perfectly wrap a cube with this blocky shape?

This seems to work: Below, I printed out the shape, and cut off the excess. The white parts are for glueing; if everything works out as planned, all of them will be covered by the coloured bits ...
• 77.4k
Accepted

### What percentage is grey?

A visual approach...
• 19.2k

### Simple geometry. Or is it?

I know the answer is already given but I'd like to show an easy explanation of why the 2 planes are coplanar. Take this image: Consider two pyramids sitting side by side, and draw a line between ...
• 11.2k
Accepted

### Cover 63 squares of a chess board

These should do it: Just to show another example:
• 5,190

• 21.4k

### Can you perfectly wrap a cube with this blocky shape?

The shape can be folded like this
• 14.5k
Accepted

### Six pyramids in a cube

The answer is because the volume of a pyramid is proportional to its height, and we know that each pair of opposite pyramids together has the same total height. Therefore, all three pairs of pyramids ...
• 1,999
Accepted

Explanation:
• 536
Accepted

### Help the prisoners

You can't. Color them like a checkerboard - the top-left-front cell is black, and the ones adjacent to it are white, and the ones adjacent to those are black... Each prisoner in a white cell must ...
• 146k
Accepted

### A new way to cut a pizza

This paper by Joel Haddley and Stephen Worsley answers a slightly different question - finding monohedral disc dissections where not all pieces touch the centre - but the results generally apply to ...
• 53.3k
Accepted

### Create a 3 inch measurement

I can do it in folds, by
• 4,381
Accepted

### Release the "Q" ball

Here is one possible solution to this puzzle
• 19.2k

### Folding paper into corners

I managed to make Like so:
• 21.2k

### Odd-looking circle

He has made a rapid escape from the scene because he actually didn't know what a "circle" was. No wait.
• 591
Accepted

• 5,290
Accepted

### How many matchsticks need to be removed so there are no equilateral triangles?

@hexomino's answer is correct and well-reasoned, as always. Here's another approach, which to me feels much more.. "axe-to-the-head" is what I'd call it in my native language, so I thought ...
• 77.4k
Accepted

• 13.6k
Accepted

### Find the perimeter (seemingly unsolvable problem)

Here's a non-visual solution which some may find more easy to understand than a visual solution:
• 2,319
Accepted

### A colorful dodecahedron

Partial Answer: Solution: Other Solutions: Fun Stuff:
• 8,206
Accepted

### 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 ...
• 53.3k

• 10.3k
Accepted

### Magnets on a whiteboard

This is a solution
• 814

### Two chunky pixelated X's locked in mortal combat!

The combined area of the X's is The solution:
• 14.9k
Accepted

### 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'...
• 77.4k

### Find the perimeter (seemingly unsolvable problem)

To me the most visually intuitive solution is as follows: First of all, Then take
• 19.2k
Accepted

### Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

I think the answer is Consider the following image: Generalizing this result, the question "For which $n$ can an $n \times n$ square be tiled with $2 \times 2$ and $3 \times 3$ squares?" ...
• 14.1k

Only top scored, non community-wiki answers of a minimum length are eligible