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.