These two games are played with coins. Find strategies for winning each game and

Question

These two games are played with coins. Find strategies for winning each game and justify as much as you can.

a) There are two players who each start with a large supply of pennies. Players take turns placing 1, 2, 3, 4, or 5 pennies in a pile. The first person to make the value of the pile reach or exceed $1 (100 pennies) wins.

b) There are two players who each start with a large supply of pennies (1 cent), nickels (5 cents), and dimes (10 cents). Players take turns placing one coin in the pile; either a penny, a nickel, or a dime. The first person to make the value of the pile reach or exceed $1 (100 cents) wins.

Explanation / Answer

a)

winning strategy ,

become player 1 pick 4 first

let x be the value picked by player 2 and y be the value picked by you next

y = 6-x,

100 = 96 + 4

since you already picked4 first

and you are always taking pennies such that sum is 6 ,

you will win

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