SOLUTIONS - Springer
(German Mathematical Olympiad, 1985) 5. Arguing by contradiction, let us assume that the area of the overlap of any two sur-faces is less than 1 9. In this case, if S 1,S 2,...,S n denote the nine surfaces, then the area of S 1 ∪S 2 is greater than 1 +8 9, the area of S 1 ∪S 2 ∪S 3 is greater than 1 +8 9 +7 9,..., and the area of S 1 ∪S ...
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