1010 Cycle decompositions
39.3 Dudeney’s Canterbury puzzle
Take nine counters numbered 1 to 9, and place them in a row
in the natural order. It is required in as few exchanges of pairs
as possible to convert this into a square number. As an ex-
ample in six moves we give the following: (7846932), which
give the number 139854276, which is the square of 11826.
But it can be done in much fewer moves.
The square of 12543 can be found in four moves, as follows.
123456789
(25) 153426789
(37) 157426389
(38) 157426839
(34) 157326849
The squares of 25572, 26733, and 27273 can also be obtained in four
moves.
- 123456789
653927184
•
123456789
714653289
•
123456789
743816529
(^1) Puzzle 128 of [Dudeney]