squares and busses
Source: 2015 Flanders Mathematical Olympiad, Problem 3
April 27, 2015
combinatorics
Problem Statement
A group of people is divided over two busses in such a way that there are as many seats in total as people. The chance that two friends are seated on the same bus is .
a) Show that the number of people in the group is a square.
b) Show that the number of seats on each bus is a triangular number.