hard task

[klawesyn28]

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

[Werg22]

Hint: List all the possibilities. But I don't think that is effective...

[klawesyn28]

I think that the answer is 4^5 but i don't know how to prove it.