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How to Override a private set property?

The set {3,5 , 9, 29 } has the property that the sum of any three of its?

  • Answer:

    If we check their remainder with 3, we have five numbers from the set: {0, 1, 2}. If there are three of a kind: their sum is divisible by three(thus not prime)(can't be 3, because it would be 1+1+1, which are not distinct). If there aren't three of a kind: there is at least one from each kind: we pick these(one from each):(0+1+2) this is divisible by three, and can't be 3: thus not prime.

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If we check their remainder with 3, we have five numbers from the set: {0, 1, 2}. If there are three of a kind: their sum is divisible by three(thus not prime)(can't be 3, because it would be 1+1+1, which are not distinct). If there aren't three of a kind: there is at least one from each kind: we pick these(one from each):(0+1+2) this is divisible by three, and can't be 3: thus not prime.

Peter

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