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
There are five pairs of brackets, and 5 from 22 gives the number of
changes required : 17.