, 2011

Isaac has a large supply of counters, and places one in each of the $1 \times 1$ squares of an $8 \times 8$ chessboard. Each counter is either red, white or blue. A particular pattern of coloured counters is called an arrangement. Determine whether there are more arrangements which contain an even number of red counters or more arrangements which contain an odd number of red counters. Note that $0$ is an even number.