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

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

Squaring the Digits

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.

As an example in $6$ pairs we give the following:

$\tuple {7, 8}$ (exchanging $7$ and $8$),

$\tuple {8, 4}$, $\tuple {4, 6}$, $\tuple {6, 9}$, $\tuple {9, 3}$, $\tuple {3, 2}$, which gives us the number $139 \, 854 \, 276$,

which is the square of $11 \, 826$.

But it can be done in much fewer moves.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $91$. -- Squaring the Digits
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $128$. Squaring the Digits