This is the coolest math question I've seen in a while.

"Given an $n$-dimensional chess board $\mathbb Z_n$, and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite number of moves?

To avoid trivial exceptions, assume the king starts a very large distance away from the nearest rook.

Rooks can change one coordinate to anything. King can change any set of coordinates by one.

And same problem with i) Bishops and ii) Queens, in place of rooks."

Question

This is the coolest math question I've seen in a while.

"Given an $n$-dimensional chess board $\mathbb Z_n$, and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite number of moves?

To avoid trivial exceptions, assume the king starts a very large distance away from the nearest rook.

Rooks can change one coordinate to anything. King can change any set of coordinates by one.

And same problem with i) Bishops and ii) Queens, in place of rooks."

experimentx · Answer

depends on where the king is .. if king were in the corner ... i would say 2 moves

anonymous · Answer

That would be a trivial exception. The king is starting the largest distance away from the nearest rook, and assuming equal sides, he's in the center.

experimentx · Answer

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