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Nonempty subset proof

  1. Apr 11, 2005 #1
    No idea where to start with this one...to prove that it is not possible to have a set B of 5 distinct positive single-digit integers such that every possible nonempty subset of B has a different sum. How do I approach it/do it?
     
  2. jcsd
  3. Apr 11, 2005 #2

    matt grime

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    Given 5 distinct numbers, there are 2^5 - 1 possible sums of subsets, excluding the sum of all 5 which is 31.

    However, the biggest possible sum of 4 distinct single digit numbres is 9+8+7+6= 28, so apply the pigeon hole principle.
     
  4. Apr 11, 2005 #3
    I'll try that, thanks for the suggestion!
     
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