ASU 285 All Soviet Union MO 1980 strips inside a square
Source:
July 19, 2019
combinatoricscombinatorial geometrySum
Problem Statement
The vertical side of a square is divided onto segments. The sum of the segments with even numbers lengths equals to the sum of the segments with odd numbers lengths. lines parallel to the horizontal sides are drawn from the segments ends, and, thus, strips are obtained. The diagonal is drawn from the lower left corner to the upper right one. This diagonal divides every strip onto left and right parts. Prove that the sum of the left parts of odd strips areas equals to the sum of the right parts of even strips areas.