Problem of the Week 1026

Quartets

Four squares on a chessboard are called a quartet if their centers form a rectangle with sides parallel to the sides of the board. Note that the quartet consists ONLY of the four squares, not any that might lie inside.

What is the maximum number of pairwise disjoint quartets that can fit on a 25×25 board? Of course, this maximum cannot be more than 156, since 4 × 157 = 628 > 625 = 25².

Source: Latvian Olympiad 2000; Crux Math. Nov. 2004. p. 415.

© Copyright 2005 Stan Wagon. Reproduced with permission.