Seth has nine stones: three painted blue, three painted red and three painted yellow. The blue stones are labelled , , , as are the red stones and the yellow stones. He builds a vertical tower with three stones.
Three stones form a set if they all have the same colour, all have the same number, all have different colours, or all have different numbers.
In how many ways can he build a tower that avoids creating a set?
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Cayley Mathematical Olympiad (2022)
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