Henry Ernest Dudeney/Puzzles and Curious Problems/94 - Simple Multiplication/Solution

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