The Discover Boggler By Scott Kim

Sep 1999

Rogue Knights There is a classic recreational mathematics called the eight queens problem. The challenge is to place eight queens on a chessboard so no two attack each other. There are several solutions. In high school I thought up a nice generalization: place as many queens as possible on a chessboard so each attacks exactly one other queen. Or two, three or four. More than four isn't possible. Martin Gardner published this problem in his 1981 column about my work in Scientific American magazine, later reprinted in his book The Last Recreations. While working on the queens problem I also happened to try placing knights on a chessboard, and came up with the problem that appears in Discover as problem 5: place knights on a 7x7 board so that each attacks exactly four others. Pleasingly, the lines of attack form the edges of hypercube. Years later I revisited this puzzle and wondered what would happen each knight attached 0, 1, 2 or 3 others. I was happy to find that this puzzle is just as interesting as the queens puzzle. Here is a complete list of the best known solutions on different sized boards.

Copyright 2000 Scott Kim. All rights reserved.