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.
When they start with twenty discs numbered from 1 to 20 it is impossible for them to share them this way. Which of the numbered discs makes the task impossible?
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Hamilton Mathematical Olympiad 2020 (2020)
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