41
votes
Accepted
7
votes
16 queens puzzle
For the question of maximizing the number of sets of $8$ queens, define a graph with a node for each of the $92$ solutions for $8$ queens and an edge for each pair of solutions that share a cell. Now ...
- 11.5k
6
votes
Accepted
6
votes
A colorful dodecahedron
Designing the puzzle took much more effort than solving it. While the mirror symmetrical solution can be found manually, for a complete survey a computer aided search is necessary. This can be done ...
- 1,515
5
votes
How many 4x4 Latin Squares are there?
For any solution, we can relabel the numbers so that the top row reads 1,2,3,4. Given that, there are only
This means there are
- 50.3k
5
votes
5
votes
Accepted
3
votes
Accepted
Tile 1x2 dominoes in a 2x10 space
Answer:
Solution:
Suppose that a $2\times N$ space can be tiled in $f(N)$ ways.
Bonus:
Bonus, alternate solution:
Suppose that a $2\times N$ space can be tiled in $g(N)$ ways with identical painted ...
- 578
2
votes
Permutations with given longest increasing subsequence
Here is the general idea:
I then wrote a Java computer program
- 31.6k
2
votes
A colorful dodecahedron
I wrote a program to enumerate the ways the pentagons can be rotated and placed into a Dodecahedron net like the one illustrated in @DqwertyC's solution. I get
But this overcounts the number of ...
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