Question 3
Let $m,n$ be positive integers and let $\mathcal R$ be a $2m\times2n$ grid of unit squares. A domino is a $1\times2$ or $2\times1$ rectangle. An up-right path goes from the lower-left corner to the upper-right corner using exactly $2m+2n$ grid edges. Find the number of these paths dividing $\mathcal R$ into two possibly empty subsets, each tileable with dominoes.
Proposed by Wilbert Chu.
Manual essay; 1 editorial point, not official contest scoring.
Proposed by Wilbert Chu.
Manual essay; 1 editorial point, not official contest scoring.