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Problem of the Week 904

Random Queens

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If two queens are randomly placed on distinct squares of an ordinary chessboard, what is the probability that they attack each other?

Note: A chessboard has 8 rows and 8 columns; a queen attacks in all directions; in other words, she can move any number of squares in any row, column, or diagonal that contains her square.

Source: This classical problem appeared on the first Konhauser Problemfest in 1993. The Konhauser Problemfest is a mathematical team competition with teams from Carleton College, Gustavus Adolphus College, Macalester College, Saint Olaf College, and the University of Saint Thomas. The 8th Konhauser Problemfest will be held Saturday, February 26, at Macalester College.
© Copyright 2000 Stan Wagon. Reproduced with permission.

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15 February 2000