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Given the set of integers {1,2,3,…,801}, what is the maximum number of sets we could distribute these numbers into such that the sum of each set is exactly the same.

  • Maths -

    If we sum the sequence,
    S=&sum i, i=1,801, we have
    S=3²*89*401, as prime factorization.
    Thus the largest number of groups is 401 sets, each sum would therefore be 801, as follows:
    {1,800},{2,799}...{399,402},{400,401},{801} for a total of 401 sets.

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