Combinatorics › Distributing objects › Distributing objects into boxes
Maximum elephants with a unique distribution
High school · ●●●○○ 50 pts
Ostap Bender organized an elephant giveaway in the city of Fux. 28 union members and 37 non-members showed up, and Ostap distributed the elephants so that all union members received the same number of elephants and all non-members received the same number of elephants (the two numbers may differ). It turned out that there was only one way to distribute the elephants so that all of them were given away. What is the maximum number of elephants Ostap Bender could have had? (Each person who came received at least one elephant.)