# Combinatorics, Algorithm, and Humanity

a lovely story on combinatorics problem, algorithm, and humanity.

- 1
- 2
- 12
- 184
- 8512
- 1262816
- 575780564
- 789360053252
- 3266598486981642
- 41044208702632496804
- 1568758030464750013214100
- 182413291514248049241470885236
- 64528039343270018963357185158482118
- 69450664761521361664274701548907358996488

the sequence is “Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid.” , sequence id A007764, see https://oeis.org/A007764

there isn't a closed form formula know so far. We have counted up to f[26].

This problem, seems to be spurred by a computer game named The Witness.

[ The Witness (2016 video game) ] [ 2016-03-09 https://en.wikipedia.org/wiki/The_Witness_%282016_video_game%29 ]