Rooks on a Chessboard
Source: ToT - 2001 Fall Junior A-Level #5
August 17, 2011
combinatorics unsolvedcombinatorics
Problem Statement
Alex places a rook on any square of an empty chessboard. Then he places additional rooks one rook at a time, each attacking an odd number of rooks which are already on the board. A rook attacks to the left, to the right, above and below, and only the first rook in each direction. What is the maximum number of rooks Alex can place on the chessboard?