Answers to last week's challenges
Each player can take biscuits in one of two ways:
By taking any number they like from just one jar or
By taking the same amount from both jars.
The winner is the person who takes the last biscuit/s.
Play the game several times.
Can you find a winning strategy?
Can you always win?
Janesse's Answer:
To win:
It is the opponent's turn and there are 2 cookies in one of the jars and 1 cookie in the other.
- Case 1: The opponent takes 1 from the jar with 1. When it's your turn, you take the remaining 2. So, you will win.
- Case 2 : The opponent takes 2 from the jar with 2. When it's your turn, you take the remaining 1, you will then win.
- Case 3 : The opponent takes 1 from each jar. When it's your turn, you take the remaining 1, making you win.
- Case 4 : The opponent takes 1 from the jar with 2. When it's your turn, you take a 1 from each jar, and again, you will win.
No matter what your opponent tries to do when there are 2 cookies in one of the jars and 1 cookie in the other, you will always win.
Fion's Answer: