A puzzle by A. Vasin from the July-August 1993 issue of Quantum:

Two numbers are mirror numbers if each presents the digits of the other in reverse order, such as 123 and 321. Find two mirror numbers whose product is 92,565.

| SelectClick for Answer | | --- | | This solution is by V. Dubrovsky. The size of the product shows that the factors must have three digits each. So let one of them be abc (or 100a + 10b + c) and the other be cba. The product ends in 5, so either a or c must be 5. Say that’s a. The other factor starts with 5, and 92,565 / 500 < 200, so c must be 1. As to b, we can see that the 6 in 92,565 is the last digit of 5b + b, or 6b, so b must be either 1 or 6, and we can test these candidates to learn that it’s 6. The numbers we seek are 561 and 165. |

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