A shortsighted rook is a rook that attacks all squares in the same column and in the same row for which he can not go more than 60steps.
What is the maximal amount of shortsighted rooks that don't attack each other that can be put on a 100×100 chessboard.
(In reply to
Solution (?) by Steve Herman)
I don't think this can be beaten, but there are quite a few ways to accomplish it.
Take the top right square of 39 rows and columns. This can be populated with 39 rooks in 39! ways.
The other three corners can be populated in the exact same pattern.
This leaves a central 22x22 square which can be populated in 22! ways.
(There are four 39x22 rectangles centered on the sides which can contain no rooks.)
Total number of rooks = 39*4+22=178
Total number of solutions = 39!*22!=2.29*10^67 not counting the very few that would be reflections or rotations of each other.

Posted by Jer
on 20210405 14:08:53 