In a rock-paper-scissors round robin tournament any two contestants play against each other ten times in a row. Each contestant has a favourite strategy, which is a fixed sequence of ten hands (for example, RRSPPRSPPS), which they play against all other contestants. At the end of the tournament it turned out that every player won at least one hand (out of the ten) against any other player.
Prove that at most 1024 contestants participated in the tournament.Submitted by Dávid Matolcsi, Budapest combinatoricslinear algebra