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eight different symbols

Source: 8-th Taiwanese Mathematical Olympiad 1999

January 22, 2007
inductioncombinatorics unsolvedcombinatorics

Problem Statement

There are eight different symbols designed on n≥2n\geq 2 different T-shirts. Each shirt contains at least one symbol, and no two shirts contain all the same symbols. Suppose that for any kk symbols (1≤k≤7)(1\leq k\leq 7) the number of shirts containing at least one of the kk symbols is even. Determine the value of nn.
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