# Tag Info

### What is the least number of colours Peter could use to color the 3x3 square?

As described in many answers, five colors is the minimum. Here we bring in the theory of pandiagonal Latin squares to show some hidden features of the solution and allow a generalization to $n×n$ ...
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### What is the least number of colours Peter could use to color the 3x3 square?

Basically a beginner here. Start with a diagonal. All three cells must have unique colours: Then, the two unshaded corners must be given unique colours because both of them have a diagonal with the ...
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### What is the least number of colours Peter could use to color the 3x3 square?

I got by "coloring" with numbers:
Accepted

### What is the least number of colours Peter could use to color the 3x3 square?

The minimum is because
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### Packing cubes into spheres

Some empirical evidence that n=6 The best axis-aligned configuration I found uses a radius of $1.630998544...$. Here's configuration with $6$ cubes that fits in a sphere with radius ~$1.627$. (The ...
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### Fitting the 9th piece into the pizza box

I just wrote an HTML canvas here: Picture: HTML: ...
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1 vote

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### Use all eight of the given polygons to tile a parallelogram

The total area of all tiles together is With that in mind it doesn't take much time to find:
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### Fitting the 9th piece into the pizza box

This is not a proper answer, just for fun.
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### Fitting the 9th piece into the pizza box

The first approach to this problem is to see if it is possible at all, and so the first, most trivial idea is to inscribe a circle within the 2x2 square (b/c you want to keep the shapes as close as ...
Accepted

### Fitting the 9th piece into the pizza box

Timely question. I did this just last night: Desmos:
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### Discrete cops and robbers

The cop wins up to and including diameter which is the diameter of the circumcircle of a If the diameter is larger the robber wins by Conversely, if the diameter is equal or smaller A recipe for ...
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### Discrete cops and robbers

The answer is invalid because I read the question wrong: For which values of d can the cop catch the robber in a finite number of turns and how? For which values of d can the robber evade the cop ...
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### Cutting a 27×27 square into incomparable rectangles

The widths and heights of the rectangles are: They tile the square:
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