Henry Ernest Dudeney/Puzzles and Curious Problems/91 - Squaring the Digits/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $91$

Take $9$ counters numbered $1$ to $9$, and place them in a row: $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$.

It is required in as few exchanges of pairs as possible to convert this into a square number.

A $3$-move solution is:

$\tuple {1, 5}$, $\tuple {8, 4}$, $\tuple {4, 6}$

which gives us:

$513 \, 814 \, 769 = 22 \, 887^2$

For interest's sake, we also offer up the $4$-move solution given by Dudeney:

$\tuple {7, 3}$, $\tuple {3, 4}$, $\tuple {4, 8}$, $\tuple {2, 5}$

which gives us:

$157 \, 326 \, 849 = 12 \, 543^2$