Maths Olympiad Prep

Track / Stage 5 / 66 of 400 #666 of 1964

Problem 666

AIME late
Combinatorics Difficulty 5.2 Find the answer

22. How many different positions can appear on a chessboard if both players, starting from the initial position, make only one move each?

A number or a short expression. Spacing and $ signs are ignored.

Official solution

22. In the initial position, each pawn and each knight can move in two ways, while the other pieces cannot make a move. Therefore, from the initial position, 20 different moves can be made by both the white and black pieces. Thus, after each player makes one move, 2020=40020 \cdot 20=400 different positions can result.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.