22
votes
Accepted
What is the least number of colours Peter could use to color the 3x3 square?
The minimum is
because
- 28.2k
21
votes
Accepted
Fitting 10 pieces of pizza in a box
Thanks to 2012rcampion for crunching the numbers to find a minimum side length of
For this arrangement of slices:
- 16.8k
18
votes
Fitting 10 pieces of pizza in a box
Here is a simple but rather effective packing:
The sides of the square box are
Explanation:
- 7,745
16
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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 ...
- 550
15
votes
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:
- 7,745
8
votes
Packing cubes into spheres
(partial answer)
Simplification
Let's start with an intuitive simplification. The cubes must be stacked in independent "layers", where each layer "sits" on $y=k$ for some integer $...
- 2,213
7
votes
Accepted
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 ...
- 2,213
7
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Fitting 10 pieces of pizza in a box
Here's the best setup I could come up with, using unit slices:
Achieving a length of
Here, the highlighted slice is shifted by $b \approx 0.01626$ in both directions, and the rest of the pieces fit.
...
- 1,086
7
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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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4
votes
What is the least number of colours Peter could use to color the 3x3 square?
I got
by "coloring" with numbers:
- 231
3
votes
Accepted
2
votes
1
vote
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