MathDB

In a chess tournament there are

n \geq 5

players, and they have already played

\left[ \frac{n^2}{4} \right] +2

games (each pair have played each other at most once).
(a) Prove that there are five players

a, b, c, d, e

for which the pairs

ab, ac, bc, ad, ae, de

have already played.
(b) Is the statement also valid for the

\left[ \frac{n^2}{4} \right] +1

games played?
Make the proof by induction over

n.

Problem Statement