Question 17
Albert and Betty play the following game. There are two bowls on a table; a red bowl and a blue bowl. At the beginning of the game there are $100$ blue balls in the red bowl and $100$ red balls in the blue bowl. In each turn a player must take one of the following moves:
a) Take two balls of different colors from one bowl and throw the balls away.
b) Take two red balls from the blue bowl and put them in the red bowl.
c) Take two blue balls from the red bowl and put them in the blue bowl.
They take turns alternately, and Albert starts. The player who first takes the last red ball from the blue bowl or the last blue ball from the red bowl wins. Determine who has a winning strategy.
a) Take two balls of different colors from one bowl and throw the balls away.
b) Take two red balls from the blue bowl and put them in the red bowl.
c) Take two blue balls from the red bowl and put them in the blue bowl.
They take turns alternately, and Albert starts. The player who first takes the last red ball from the blue bowl or the last blue ball from the red bowl wins. Determine who has a winning strategy.