What is the maximum difference between adjacent numbers among those whose sum of digits is divisible by 7?

#
Let's first prove that this difference cannot be greater than 13. Indeed, among 13 consecutive natural numbers, the sum of the digits of at least one of them is divisible by 7, since among 13 consecutive natural numbers, at least 7 lie in the same decade. Then, the sums of the digits of these seven numbers are consecutive natural numbers, which means that among them, there is a number divisible by seven. Therefore, the desired number is no more than 13. However, between the numbers 993 and 1006, there are no other numbers whose sum of digits is divisible by seven, and 1006 - 993 = 13. Thus, the desired difference is 13.

## Answer

13.00

Send a comment