# Five balls in a scale

Suppose that I have 5 balls with different weights. A scale tells me which one ball is heavier than another. I have to write down the the pairs of balls I use before I use the scale. Is it possible to write down at most nine pair of balls which tells me the order of balls weights?

I guess the answer is no as 4+3+2+1=10>9 but I have no proof.

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You must know the number of different pairs you can do with $5$ balls (the minimal number of checks) which is $$\frac{5!}{2!.(5-2)!}=10$$