IrMO 2013 Problem 4

Each of the $36$ squares of a $6 \times 6$ table is to be coloured either Red, Yellow or Blue. (a) No row or column is contain more than two squares of the same colour. (b) In any four squares obtained by intersecting two rows with two columns, no colour is to occur exactly three times. In how many dierent ways can the table be coloured if both of these rules are to be respected?