How Many Participants Can Have Unique Task Scores in a Math Competition?

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SUMMARY

The discussion centers on determining the maximum number of participants in a math competition who can achieve unique task scores across six tasks, where each task can yield scores of 6, 5, 3, or 0. The key insight is that for every pair of participants, there exist two tasks where their scores differ. The proposed solution suggests that the maximum number of participants is 4^5, which equals 1024, based on the combinatorial possibilities of score assignments. A formal proof is needed to validate this conclusion.

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klawesyn28
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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
possible.

Could anybody help me?

Thanks in advance
 
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Hint: List all the possibilities. But I don't think that is effective...
 
Last edited:
I think that the answer is 4^5 but i don't know how to prove it.
 

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