(related to Problem: Arranging The Jampots)
Two of the pots, $13$ and $19,$ were in their proper places. As every interchange may result in a pot being put in its place, it is clear that twenty-two interchanges will get them all in order. But this number of moves is not the fewest possible, the correct answer being seventeen. Exchange the following pairs: $(3-1, 2-3),$ $(15-4, 16-15),$ $(17-7, 20-17),$ $(24-10, 11-24, 12-11),$ $(8-5, 6-8, 21-6, 23-21,$ $22-23, 14-22, 9-14,$ $18-9).$ When you have made the interchanges within any pair of brackets, all numbers within those brackets are in their places. There are five pairs of brackets, and $5$ from $22$ gives the number of changes required — $17.$
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