Soviet Union 9
Source: IMO LongList 1959-1966 Problem 52
September 2, 2004
geometrycombinatoricsareacombinatorial geometrydissectionIMO ShortlistIMO Longlist
Problem Statement
A figure with area is cut out of paper. We divide this figure into parts and color them in different colors. Now, we turn around the piece of paper, divide the same figure on the other side of the paper in parts again (in some different way). Show that we can color these new parts in the same colors again (hereby, different parts should have different colors) such that the sum of the areas of all parts of the figure colored with the same color on both sides is