The following problem (link in german) January 2010 is part of this years mathematics competition of Baden-Württemberg for pupils at the age of 10-12.

Prove that you cannot get 50 as the sum of exactly 5 numbers from the set {5,9,13,17,19}.

Prove that there are exactly 2 ways to get 50 as the sum of exactly 5 numbers from the set {6,11,13,15,17}.

Nice problem with a nice solution. Albeit maybe a little hard at that age.

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