Question 3
Let $b,w\ge2$ be integers and $n=b+w$. Assemble a regular $2n$-gon from $2b$ black and $2w$ white unit rods so that parallel sides have the same color. Translate the black rods to form a convex $2b$-gon $B$, and the white rods to form a convex $2w$-gon $W$. Prove that $[B]-[W]$ depends only on $b,w$, not the assembly. The source example has $b=3,w=2$.
Proposed by Ankan Bhattacharya. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24775345. One point is a nonofficial editorial normalization; this essay requires manual grading.
Proposed by Ankan Bhattacharya. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24775345. One point is a nonofficial editorial normalization; this essay requires manual grading.