2023 SSMO Relay Round 2 Problems/Problem 3

Revision as of 21:29, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T=</math> TNYWR. In a committee of <math>2023</math> people, <math>N</math> are scientists and the rest are builders. In order to make a building, <math>...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $T=$ TNYWR. In a committee of $2023$ people, $N$ are scientists and the rest are builders. In order to make a building, $\frac{N}{2}$ people must be choosen with at least one scientist and one builder. If $x$ is the number of ways to do this, find the largest integer $a$ such $2^a \mid x$.

Solution