MathDB
2013 Fall Team #8

Source:

March 26, 2022
combinatorics

Problem Statement

Two kids AA and BB play a game as follows: from a box containing nn marbles (n>1n > 1), they alternately take some marbles for themselves, such that: 1. AA goes first. 2. The number of marbles taken by AA in his first turn, denoted by kk, must be between 11 and nāˆ’1n - 1, inclusive. 3. The number of marbles taken in a turn by any player must be between 11 and kk, inclusive. The winner is the one who takes the last marble. Determine all natural numbers nn for which AA has a winning strategy