Two players (White and Black) are playing on an infinite chess board (extending infinitely in all directions). First, White places a certain number of queens (and no other pieces) on the board. Black then places a king on any unoccupied, unattacked square of the board. The players take turns moving until Black is checkmated. What is the minimum number of queens White needs to force a checkmate? Answer the same problem if White starts with rooks instead of queens. Do the same for bishops and knights. Let Q, R, B, and N be the minimum number of queens, rooks, bishops, and knights, respectively. What is the sum 1/Q + 1/R + 1/B + 1/N?
This problem appeared as the IBM Research "Ponder This" challenge of December 2011. The problem and solution may be found at: http://domino.research.ibm.com/comm/wwwr_ponder.nsf/challenges/December2011.html
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