MathDB

3

Part of 2015 Flanders Math Olympiad

Problems(1)

squares and busses

Source: 2015 Flanders Mathematical Olympiad, Problem 3

4/27/2015
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 12\frac{1}{2}. 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.
combinatorics