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11. (6 Pts.) Show that if we split any 11 numbers in 5 sets, then there...

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Advance Math

11. (6 Pts.) Show that if we split any 11 numbers in 5 sets,then there exists one set that contains a subset such
that the sum of its elements is a multiple of 3.

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4.3 Ratings (761 Votes)
Let be any integersCase I If some divides one of say then the set that contains has as its subset and the sum of all elements in is just a multiple of Case II Suppose for all Since sets contains integers by Pigeonhole    See Answer
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