Problem of the Week 1053

Triskaidekaphobics Beware

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How many consecutive positive integers can you find so that none of the digit-sums (base 10) are divisible by 13?

Note: Because 49 is the first integer whose digit-sum is divisible by 13, the 48 integers from 1 to 48 meet the condition.

Source: Problem A248 Crux Mathematicorum, May 2001 p. 260.

© Copyright 2006 Stan Wagon. Reproduced with permission.