Zola and Ron play a game by alternately moving a single ten cent coin on a circular board. The game starts with the ten cent coin already on the board as shown. A player may move the coin either clockwise one position or one position toward the centre, but cannot move to a position that has been previously occupied.
The last person who is able to move wins the game.
If Zola starts, which player can play in a way that guarantees a win?
Explain this player's winning strategy.
Since the game must end (finite number of blocks and can't play on a previously occupied block) and only one person can move last, there will be a winner and hence a winning strategy.
We claim that the first player (Zola) has the winning strategy and it is to always move clockwise. There are positions left in the outer ring so only player (Zola) can complete the outer ring and then player (Ron) will be forced to go inwards. Note at any stage player (Ron) can opt to go inwards, but if he moves inwards, there will be positions left in that ring and again only player (Zola) can complete that ring. This is the same for each ring. Hence only player (Zola) can complete the inner ring and move last and hence win.