MathDB

6

Part of 2001 Mexico National Olympiad

Problems(1)

n rare coins of denominations 1,2,.., n into 5 boxes unter 4 conditions

Source: Mexican Mathematical Olympiad 2001 OMM P6

7/30/2018
A collector of rare coins has coins of denominations 1,2,...,n1, 2,..., n (several coins for each denomination). He wishes to put the coins into 55 boxes so that: (1) in each box there is at most one coin of each denomination; (2) each box has the same number of coins and the same denomination total; (3) any two boxes contain all the denominations; (4) no denomination is in all 55 boxes. For which nn is this possible?
combinatoricscoins