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Hard task

  1. Sep 21, 2005 #1
    I don't know how to solve this task:

    Participants of math competition are solving six tasks. For each task
    you can get one of marks - 6,5, 3 or 0 .
    It transpired that for each pair of participants we can indicate two
    tasks , that in each of them participant A got different mark from
    participant B.
    Delimit the highest number of participants for which this situation is

    Could anybody help me?

    Thanks in advance
  2. jcsd
  3. Sep 21, 2005 #2
    Hint: List all the possibilities. But I don't think that is effective...
    Last edited: Sep 21, 2005
  4. Sep 22, 2005 #3
    I think that the answer is 4^5 but i don't know how to prove it.
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