Imagine a black chess king on a 4D chessboard. 8 by 8 by 8 by 8 hypercubes. How many white queens do you need to mate this king, which tries to escape, of course. White doesn’t have a king, just the minimal necessary pack of queens. What is the mating algorithm? Legal moves are analogous to those of 2D chess.
Discussion over there:
http://lesswrong.com/lw/p8a/open_thread_july_10_july_16_2017/dv76
protokol2020 
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Queens can move n spaces in up to 2 dimensions or up to 4?
Queens can move along 4 dimensions and diagonally.