My grandson makes wall hangings by stitching together 16 square patches of fabric into a 4 × 4 grid. I asked him to use patches of red, blue, green and yellow, but to ensure that no patch touches another of the same colour, not even di- agonally. The picture shows an attempt which fails only because two yellow patches touch diagonally. In how many different ways can my grandson choose to arrange the coloured patches correctly?
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Australian Mathematics Competition 2020 - Junior (2020)
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