Question 52
(USS) 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 $0.1$.