Henry Ernest Dudeney/Puzzles and Curious Problems/91 - Squaring the Digits
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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.
Click here for solution
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