(a) You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
(b) It is now only required that all the rows and columns have an even number of red counters. Are there any additional solutions? Two solutions are considered the same if one can be transformed to the other by rotating the square.