Question 6
Three boxes, $V,N$ and $M$, initially contain $20,25$ and $60$ identical marbles, respectively. Two players take turns playing a game. On each turn, a player chooses one box and removes a positive number of marbles from it. However, the following conditions must always remain satisfied after each move:
- The number of marbles in box $V$ must never exceed that in box $N$;
- The number of marbles in box $N$ must never exceed that in box $M$.
The player who takes the last marble wins. One of the players has a winning strategy. Formulate a winning strategy for this player and prove that is works.
- The number of marbles in box $V$ must never exceed that in box $N$;
- The number of marbles in box $N$ must never exceed that in box $M$.
The player who takes the last marble wins. One of the players has a winning strategy. Formulate a winning strategy for this player and prove that is works.