Arun and Disha have some numbered discs to share out between them. They want to end up with one pile each, not necessarily of the same size, where Arun’s pile contains exactly one disc numbered with a multiple of 2 and Disha’s pile contains exactly one disc numbered with a multiple of 3.
Count the number of ways of sharing the discs when they start with ten discs numbered from 1 to 10.
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Hamilton Mathematical Olympiad 2020 (2020)
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