In how many different ways can the opening pair of moves be made in a game of chess - one white move followed by one black move.

At the very start of a chess game, the sheer number of possibilities is already impressive. The calculation begins by looking at all the legal moves for the white pieces. Each of the eight pawns can move either one or two squares forward, accounting for sixteen different moves. Additionally, each of the two knights can leap over the pawns to two possible squares, adding another four moves. This brings the total number of distinct opening moves for White to exactly twenty.

Since the board is perfectly symmetrical at the beginning, Black has the exact same set of twenty possible moves to choose from as a response. To find the total number of unique opening pairs, we apply a simple principle of combinatorics: for every one of White's 20 choices, Black has 20 independent replies. By multiplying White's possibilities by Black's, we arrive at the grand total of 400 different ways a chess game can begin after just one move from each side.

This number forms the basis of what is known as opening theory, the extensive study of the game's initial phases. While 400 positions are technically possible, only a small handful of these openings, like the King's Pawn or Queen's Gambit, are regularly used in competitive play as they are considered to offer the best strategic chances.