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Maximum possible subsets

Posted on: September 24th, 2013 by
3

Suppose you have 100 integers whose sum is 1. What is the maximum number of subsets whose sum is positive?

via AMS puzzle corner 14


3 Responses to Maximum possible subsets

  1. Sid Hollander had this to say about that:

    Sum 2^n as n goes from 0 to 99. The 100th sum would be the inverse of each sum in the first.

  2. Lizard had this to say about that:

    Regardless of the numbers chosen, exactly half of the subsets will have positive sum. Pair each subset with its complement and note that if a + b = 1 then exactly one of a and b is positive.

  3. Sid Hollander had this to say about that:

    If S is the set are there 98 subsets with sum =1 i.e(1+0)

    S = (0,-97,1,1,1,......,1)


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