olymmath

Putnam 1958 B3

  • Session B
  1. In a round-robin tournament with nn players (each pair of players plays one game) in which there are no draws, the numbers of wins scored by the players are s1,s2,…,sns_{1}, s_{2}, \ldots, s_{n}. Prove that a necessary and sufficient condition for the existence of 3 players, A,B,CA, B, C, such that AA beat B,BB, B beat CC, and CC beat AA is s12+s22+⋯+sn2<(n−1)(n)(2n−1)′6s_{1}^{2}+s_{2}^{2}+\cdots+s_{n}^{2}<(n-1)(n)(2 n-1)^{\prime} 6

Dataset text PutnamGAP. Quoted with source.

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