Question 114
A natural number $n \ge 5$ will be called *special* if, no matter how we choose five distinct numbers from $1, 2, 3, \ldots, n$, we find among them four distinct numbers $a, b, c, d$ so that $a + b = c + d$.
a) Prove that $n = 6$ is special.
b) Find all the special numbers.
a) Prove that $n = 6$ is special.
b) Find all the special numbers.