Question 66
Consider a set $S$ of 2006 distinct numbers. A subset $T$ of $S$ is called stubborn if for every $u, v$ (not necessarily distinct) in $T$, the number $u + v$ does not belong to $T$. Prove that
i) if $S$ is the set of 2006 first positive integers, then the number of elements of every stubborn subset $T$ of $S$ does not exceed 1003,
ii) if $S$ consists of 2006 arbitrary positive integers then there exists a stubborn subset $T$ of $S$ having 669 elements.
i) if $S$ is the set of 2006 first positive integers, then the number of elements of every stubborn subset $T$ of $S$ does not exceed 1003,
ii) if $S$ consists of 2006 arbitrary positive integers then there exists a stubborn subset $T$ of $S$ having 669 elements.