IMO 1966 LL USS52

A figure of area 1 is cut out from a sheet of paper and divided

imolonglistmathematicsolympiad

IMO 1966 LL USS52

Origin: USS

Problem

A figure of area 1 is cut out from a sheet of paper and divided into 10 parts, each of which is colored in one of 10 colors. Then the figure is turned to the other side and again divided into 10 parts (not necessarily in the same way). Show that it is possible to color these parts in the 10 colors so that the total area of the portions of the figure both of whose sides are of the same color is at least 0.1.