Question: 1. You are given three piles with 79, 237 and 869 chocolates respectively. Two operations are allowed: (a) merge two piles together or (b) divide

1. You are given three piles with 79, 237 and 869 chocolates respectively. Two operations are allowed: (a) merge two piles together or (b) divide a pile with an even number of chocolates into two equal piles. Is there a sequence of operations that would result in 1 185 piles with one chocolate each?

2. Suppose you wish to choose 10 large integers m1, . . . , m10 such that they are pairwise relatively prime. How can you use (a) to come up with such integers?

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