TOT 1998 Autumn AJ6 gang of robbers took away a bag of coins
Source:
May 11, 2020
combinatorics
Problem Statement
A gang of robbers took away a bag of coins from a merchant . Each coin is worth an integer number of pennies. It is known that if any single coin is removed from the bag, then the remaining coins can be divided fairly among the robbers (that is, they all get coins with the same total value in pennies) . Prove that after one coin is removed, the number of the remaining coins is divisible by the number of robbers. (Folklore, modified by A Shapovalov)