Magician
Source: All Russian Mathematical Olympiad 2008. 11.6
June 13, 2008
geometryperimeteralgorithmcombinatorics proposedcombinatorics
Problem Statement
A magician should determine the area of a hidden convex -gon . In each step he chooses two points on the perimeter, whereas the chosen points can be vertices or points dividing selected sides in selected ratios. Then his helper divides the polygon into two parts by the line through these two points and announces the area of the smaller of the two parts. Show that the magician can find the area of the polygon in steps.