Question 2
To play the lottery game Sum Thing, you choose five distinct numbers from $1$ to $50$, then the lottery master chooses five distinct numbers from $1$ to $50$. If there exist a nonempty subset of your five numbers and a nonempty subset of the lottery master's five numbers such that both subsets have the same sum, then you win.
Can you choose five numbers that guarantee a win? Either demonstrate such a set, with a proof of validity, or prove that no such set exists.
Can you choose five numbers that guarantee a win? Either demonstrate such a set, with a proof of validity, or prove that no such set exists.