u/pichutarius

In a m by n chess board, place m kings on the leftmost column. Count the number of ways to move all kings to the rightmost column, such that each tile is visited at most once.

Note: a king moves one tile to one of the 8 adjacent tile.

construct a n by n table with these conditions:

1. each cell is an unordered pair.
2. each column and row contains all integers from 0 to 2n-1 exactly once.
3. no duplicate pair.

for odd n, this is relatively easy.

for even n, i cant figure out a way. i suspect there is no solution but i cannot prove it.

unrelated note: this was inspired by IRL problem that i had to solved when creating a duty time table. if you know a working solution for n=8 please show it.