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10/16/2007

August 12–August 18, 2008

Problem

All of an 8x8 chessboard, with the exception of one square, is covered by 1x3 rectangular tiles. How many of the 64 squares can occur as the uncovered square?

(For a slightly harder problem, consider tiling a 9x9 board with 1x4 tiles. Which of the 81 squares can occur as the uncovered square?)

Solution

List of solvers

Qiaochu Yuan (undergrad); Dustin Moody (graduate); Steve Wilmarth, Mike Goodman, Lloyd Sakazaki, Steven Behrend (outside).

Mike Goodman wins the prize!