Solvers to random problems
Math problem from Mera Favorit matematik 3A (ISBN 78-91-44-12427-8). Written as en exercise in showing how math and programming frees the mind to ask further questions. How hard is it typically to find a solution? How many solutions are there? How difficult are different sized boards? Are there solutions for all starting points?
Write number 1, 2, 3 and so on in the matrix, as far as possible.
- You choose which element to start in
- You may move over two (2) squares horizontally or vertically or over one (1) square diagonally, see example below
- Follow the rules and try to fill in all numbers
The solver supports any size of matrix, with the caveat that solutions might not exist for a given size (or take very long time to find). Typically all ~12K solutions to a 5x5 matrix are computed instantaneously, while all +2M solutions for a 6x6 matrix might take in the order of 30 minutes depending on hardware.
Sample output:
$ python3 ./number_sequence_solver.py 6 6
rate: 3.02e+06 moves/s
solutions so far: 57732
^C
You pressed Ctrl+C!
solutions so far: 58340
last solution:
1 23 12 2 22 36
33 26 7 34 27 8
11 14 29 24 13 30
6 20 17 3 21 35
32 25 10 31 28 9
18 15 5 19 16 4