Solution

(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 — $17.$

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@H-Dudeney

References

Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at http://www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.