## Question

###### Use the pigeonhole principle to solve the following problem. LetX = {0, 1, 2, 3, 4, 5, 6}. Show that for any choice of 17 subsetsof X with cardinality at most 3, at least two such subsets are suchthat their elements sum up to the same number. For instance, thesubsets {1, 2, 6} and {0, 4, 5} are such that the sum of theirelements is 9.

Use the pigeonhole principle to solve the following problem. Let X = {0, 1, 2, 3, 4, 5, 6}. Show that for any choice of 17 subsets of X with cardinality at most 3, at least two such subsets are such that their elements sum up to the same number. For instance, the subsets {1, 2, 6} and {0, 4, 5} are such that the sum of their elements is 9.

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