2013 Fall Team #8
Source:
March 26, 2022
combinatorics
Problem Statement
Two kids and play a game as follows: from a box containing marbles (), they alternately take some marbles for themselves, such that:
1. goes first.
2. The number of marbles taken by in his first turn, denoted by , must be between and , inclusive.
3. The number of marbles taken in a turn by any player must be between and , inclusive.
The winner is the one who takes the last marble. Determine all natural numbers for which has a winning strategy