Question 2
Let $m,n$ be positive integers and let $S$ be the lattice points $(x,y)$ with $1\le x\le2m$ and $1\le y\le2n$. A configuration of $mn$ axis-parallel rectangles is happy if every point of $S$ is a vertex of exactly one rectangle. Prove that the number of happy configurations is odd.
Proposed by Serena An and Claire Zhang. Source: Evan Chen’s third-party compilation; https://aops.com/community/p30216444. One editorial point; manual grading.
Proposed by Serena An and Claire Zhang. Source: Evan Chen’s third-party compilation; https://aops.com/community/p30216444. One editorial point; manual grading.