sum of digits divisible by...
Source: USSR 1961, Romanian IMO TST 1999, Problem 1
June 18, 2004
number theory solvednumber theory
Problem Statement
a) Prove that it is possible to choose one number out of any 39 consecutive positive integers, having the sum of its digits divisible by 11;
b) Find the first 38 consecutive positive integers none of which have the sum of its digits divisible by 11.