Question 3
Two people play a game with marbles in a box. They alternate turns. Each person can take one or two marbles at a time. The loser is the person who takes the last marble.
On your turn, how many marbles will you take to be sure of winning if there are:
(a) 6 marbles left;
(b) 8 marbles left;
(c) 20 marbles left?
(d) Change the rule: there are 100 marbles and each player can take 1, 2, 3 or 4 marbles per turn. You play first. How many marbles will you take to be sure of winning?
Explain how your strategy responds to the other player's later moves.
On your turn, how many marbles will you take to be sure of winning if there are:
(a) 6 marbles left;
(b) 8 marbles left;
(c) 20 marbles left?
(d) Change the rule: there are 100 marbles and each player can take 1, 2, 3 or 4 marbles per turn. You play first. How many marbles will you take to be sure of winning?
Explain how your strategy responds to the other player's later moves.