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Problem of the Week 1025

Odd Couples

Given any two digits, one can look at integers made up of those digits (using each at least once) and divisible by each of them. For example, if the digits are 2 and 4 then 24 is the smallest such number. If the digits are 2 and 5 then there is no such number, since it would have to be divisible by 10, and so have a 0. If the digits were 3 and 4, then the number is 3444.

For which pair of digits from 1,2,...,9 is this smallest number largest?

Source: Puzzles 101, by Nobuyuki Yoshigahara (AK Peters, Inc.), a collection of 101 delightful puzzles by a true master of the genre.

© Copyright 2005 Stan Wagon. Reproduced with permission.

8 February 2005