The Combinatorics and Optimization square

Perfect 9 SquareThis figure is often used as a logo for the C&O department. It is a dissection of a 33 by 32 rectangle into 9 unequal squares.

While undergraduates at Cambridge in the 1930's, Bill Tutte and threeSquaring the square friends established deep results on "squaring the square" - finding dissections of squares into squares of unequal sizes. The smallest such dissection of a square is now known to contain 21 subsquares (illustrated in the cross-stitch creation on the right by C&O PhD student Cynthia Rodriguez Villalobos). The smallest dissection of the square found by Tutte and his friends was a bit larger.