How can we know!
Alan, Ben, and Chris get together to play table tennis. They agree that the player who wins a match always stays and plays the next match with the friend who was waiting. We don't know who played the first match, but we know that Ben played 17 matches, Chris, 15 and Alan, 10. Who do we know for sure played the second match?
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1 solution
In total they played 2 1 7 + 1 5 + 1 0 = 2 1 matches. Because of what they agreed, the minimum number of matches any one of them could have played is 10. The only way to do that is to play and lose every single even match (2nd, 4th, 6th... 20th). This is how we know that Alan must have played the 2nd match.