Let S = {1, 2, . . . , 10}. Then S has 210 1 = 1023 nonempty subsets. For a nonempty
Chapter 8, Problem 30(choose chapter or problem)
Let S = {1, 2, . . . , 10}. Then S has 210 1 = 1023 nonempty subsets. For a nonempty subset Sk of S, let ak be the sum of the numbers in Sk. Show that for each collection A = {S1, S2, . . . , S10} of 10 nonempty subsets of S, there exists an integer i such that ai 0 (mod 10) or there exist two integers i and j such that ai aj (mod 10).
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