2025 Cayley Problem 25

Rita is colouring a picture of a flower. She has already coloured the centre and the stem of the flower, as shown. Next, she will colour each of the six petals with exactly one of the colours: red, orange, yellow, and blue. No two neighbouring petals can be the same colour and not all four colours need to be used. There are N different-looking ways in which Rita can colour the petals. What are the rightmost two digits of N?

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Full credit to this problem is given to the CEMC, you may view all Cayley contests here.