Henry Ernest Dudeney/Puzzles and Curious Problems/94 - Simple Multiplication/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $94$
- Simple Multiplication
* * * * * * * * * * x 2 ------------------- * * * * * * * * * *
- Substitute for the $*$ symbol each of the $10$ digits in each row,
- so arranged as to form a correct multiplication operation.
- $0$ is not to appear at the beginning or end of either answer.
Solution
1 0 9 8 7 6 5 4 3 2 x 2 ------------------- 2 1 9 7 5 3 0 8 6 4
There are many answers.
The above can be found in Pandigital Integers remaining Pandigital on Multiplication, from which we can also get:
2 1 9 7 5 3 0 8 6 4 x 2 ------------------- 4 3 9 5 0 6 1 7 2 8
4 3 9 5 0 6 1 7 2 8 x 2 ------------------- 8 7 9 0 1 2 3 4 5 6
Dudeney provides:
4 5 3 9 2 8 1 7 0 6 x 2 ------------------- 9 0 7 8 5 6 3 4 1 2
who adds:
- If you divide the first number into pairs -- $45$, $39$ etc. -- these can be arranged in any order so long as the $06$ is not at the beginning or the $45$ at the end.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $94$. -- Simple Multiplication
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $146$. Simple Multiplication