Question

Consider an infinite sequence of positions 1,2,3,... and suppose we have a stone at position 1 and another stone at position 2. In each step, we choose one of the stones and move it according to the following rule: Say we decide to move the stone at position i; if the other stone is not at any of the positions i 1,i + 2, ..., 2i, then it goes to 2i, otherwise it goes to 2i +1 For example, in the first step, if we move the stone at position 1, it will go to 3 and if we move the stone at position 2 it will go to 4. Note that, no matter how we move the stones, they will never be at the same position Use induction to prove that, for any given positive integer n, it is possible to move one of the stones to position n. For example, if n7 first we move the stone at position 1 to 3. Then, we move the stone at position 2 to 5 Finally, we move the stone at position 3 to7

Answer 1

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