The Combinatorics and Optimization square

Perfect 9 SquareThis figure is often used as a logo for the C&O department.

While undergraduates at Cambridge in the 1930's, Bill Tutte and three 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. The smallest one found by Tutte and his friends was a bit larger. A much simpler problem is to find a dissection of a rectangle into unequal squares. The smallest number of subsquares possible is 9, and this is the basis for the logo. (The logo is not square; it is actually 33 by 32.)