Imagine a round-robin chess tournament for 150 players, each of whom plays 7 games. (In other words, each player is guaranteed to participate in precisely 7 games with 7 different opponents. Remember...

Imagine a round-robin chess tournament for 150 players, each of whom plays 7 games. (In other words, each player is guaranteed to participate in precisely 7 games with 7 different opponents. Remember that each game has two players.)

There are 20 possible first moves for White in a chess game, and 20 possible first moves for Black in response. Prove that there must be two different games in the tournament that began with the same first two moves (one by White and one by Black)