sub-decks of cards, sum of cards divisible by n
Source: IMOC 2018 C6
August 16, 2021
combinatoricsnumber theory
Problem Statement
In a deck of cards, there are cards numbered from to and there are cards of each number. Now, divide this deck into sub-decks with equal sizes. Prove that if , then one could always pick cards, one from each sub-deck, such that the sum of those cards is divisible by .