TITLE: Rooks in 3D chess board
QUESTION [6 upvotes]: How many rooks are needed for a 3D chess board of size NxNxN so that every empty cube on the board can be reached by a rook in a single move?

REPLY [4 votes]: I have also seen this as the 'broken combination lock' problem, and found that a simple 'cube' visualization helped to show how the minimum number of rooks actually looks.
See http://iantotman.blogspot.ca/2014/09/the-broken-combination-lock-problem.html