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

by : $94$
* * * * * * * * * * x                 2 --- * * * * * * * * * *
 * Simple Multiplication


 * 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

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.