Consider the soda can game introduced in the class. Now suppose instead of a single circular table, there are two tables of identical size. A move consists of placing the can on any table (assuming there is a spot left on that table). Once placed, a can cannot move. The first one who cannot put a can on either table loses. In this game would you rather go first or second? Describe the winning strategy. 2) In the take-chips-away game (with normal play rules): (a) if the number of chips on the table is 15, does this represent a P-position or N-position? Describe the winning strategy. (b) if the number of chips on the table is 8, does this represent a P-position or N-position? Describe the winning strategy. 3) In the take-chips-away game (with Misère play rules): (a) if the number of chips on the table is 15, does this represent a P-position or N-position? Describe the winning strategy. (b) if the number of chips on the table is 8, does this represent a P-position or N-position? Describe the winning strategy.
1) Consider the soda can game introduced in the class. Now suppose instead of a single circular table, there are two tables of identical size. A move consists of placing the can on any table (assuming there is a spot left on that table). Once placed, a can cannot move. The first one who cannot put a can on either table loses. In this game would you rather go first or second? Describe the winning strategy.
2) In the take-chips-away game (with normal play rules):
(a) if the number of chips on the table is 15, does this represent a P-position or N-position? Describe the winning strategy.
(b) if the number of chips on the table is 8, does this represent a P-position or N-position? Describe the winning strategy.
3) In the take-chips-away game (with Misère play rules):
(a) if the number of chips on the table is 15, does this represent a P-position or N-position? Describe the winning strategy.
(b) if the number of chips on the table is 8, does this represent a P-position or N-position? Describe the winning strategy.
4) In the modified take-chips-away game (with normal play rules), we only allow for a player to take out either 1 or 2 chips (rather than up to 3). For this game:
(a) if the number of chips on the table is 15, does this represent a P-position or N-position? Describe the winning strategy.
(b) if the number of chips on the table is 8, does this represent a P-position or N-position? Describe the winning strategy.
5) Consider the game of Nim (with normal play rules):
(a) Consider piles position (3, 7) (i.e., two piles with the first pile having 3 and the second having 7 chips). Does this represent a P-position or N-position? Describe the winning strategy.
(b) Consider piles position (5, 0, 3, 2). Does this represent a P-position or N-position and why? You don't need to describe the winning strategy
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