Question

In a round-robin chess tournament, each player is paired with every other player once. The formula N = x(x - 1) / 2 models the number of chess games, N, that must be played in a round-robin chess tournament with x chess players. What does the expression x(x - 1) / 2 represent in this context?

a) The total number of players
b) The number of games played by each player
c) The number of pairings between players
d) The number of rounds in the tournament

Answer 1

In a round-robin chess tournament, the expression x(x - 1) / 2 represents the number of unique pairings between players because each player plays against every other player exactly once.

Step-by-step explanation:

The formula N = x(x - 1) / 2 represents the number of chess games, N, that must be played in a round-robin chess tournament with x chess players. The expression x(x - 1) / 2 specifically represents the number of pairings between players because each player has to play against every other player once. Since there are x players, the first player can pair with x-1 other players, the second player can then pair with x-2 remaining players (since the pairing with the first player is already counted), and so on until the last player who does not need to be paired because all possible pairings are already accounted for. The division by 2 corrects for the double counting of pairings, hence the number of unique pairings is given by this expression.