Maximum Non-Attacking Knights: Chessboard Challenge
Puzzle decsription
Suppose you have a standard chessboard with unlimited supply of knights. What’s the maximum number of knights you can place so that none of them attack each other?
Here's a quick recap of the rules of chess, a knight moves in an “L” shape, i.e., two squares in one direction and then one square either left or right. Also, a knight can attack another knight if it can reach that square in a single move.
Take a moment to experiment with different placements and see how many knights you can fit without them attacking each other.
Here’s the claim: the maximum number of knights you can place safely is 32. Can you work out exactly which 32 squares those are?
Let’s break this down. Suppose we place the first knight on any square of the chessboard. From there, the knight can move to up to eight possible positions. Notice that if the knight starts on a light square, all of its valid moves land on dark squares. Likewise, if it starts on a dark square, all of its moves land on light squares.
Author
Anurag Gupta is an M.S. graduate in Electrical and Computer Engineering from Cornell University. He also holds an M.Tech degree in Systems and Control Engineering and a B.Tech degree in Electrical Engineering from the Indian Institute of Technology, Bombay.
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