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divisor of the number of caramels remaining, as long as the divisor is strictly less than the number of caramels remaining. For example, at the start, first player could remove 1, 2, 4, 10, 20, 25, 50 caramels, but not 100 caramels. This time the game ends when exactly one caramel is left, since the only divisor of 1 is 1, which is not less than 1. The player making the move to leave exactly one caramel wins (and takes the peppermint patty as well as the last caramel). (a) Suppose Brenda lets you decide who goes first. There is a strategy to make sure you win the peppermint patty. What is it? (b) Does your strategy change if the pile of caramels starts with 101? How? (c) In part (a) what is the largest number of caramels that Brenda can take, assuming you play your strategy guaranteeing the peppermint patty?

divisor of the number of caramels remaining, as long as the divisor is strictly less than the number of caramels remaining. For example, at the start, first player could remove 1, 2, 4, 10, 20, 25, 50 caramels, but not 100 caramels. This time the game ends when exactly one caramel is left, since the only divisor of 1 is 1, which is not less than 1. The player making the move to leave exactly one caramel wins (and takes the peppermint patty as well as the last caramel). (a) Suppose Brenda lets you decide who goes first. There is a strategy to make sure you win the peppermint patty. What is it? (b) Does your strategy change if the pile of caramels starts with 101? How? (c) In part (a) what is the largest number of caramels that Brenda can take, assuming you play your strategy guaranteeing the peppermint patty?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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divisor of the number of caramels remaining, as long as the divisor is strictly less than the number of caramels remaining. For example, at the start, first player could remove 1, 2, 4, 10, 20, 25, 50 caramels, but not 100 caramels. This time the game ends when exactly one caramel is left, since the only divisor of 1 is 1, which is not less than 1. The player making the move to leave exactly one caramel wins (and takes the peppermint patty as well as the last caramel). (a) Suppose Brenda lets you decide who goes first. There is a strategy to make sure you win the peppermint patty. What is it? (b) Does your strategy change if the pile of caramels starts with 101? How? (c) In part (a) what is the largest number of caramels that Brenda can take, assuming you play your strategy guaranteeing the peppermint patty?
Transcribed Image Text:divisor of the number of caramels remaining, as long as the divisor is strictly less than the number of caramels remaining. For example, at the start, first player could remove 1, 2, 4, 10, 20, 25, 50 caramels, but not 100 caramels. This time the game ends when exactly one caramel is left, since the only divisor of 1 is 1, which is not less than 1. The player making the move to leave exactly one caramel wins (and takes the peppermint patty as well as the last caramel). (a) Suppose Brenda lets you decide who goes first. There is a strategy to make sure you win the peppermint patty. What is it? (b) Does your strategy change if the pile of caramels starts with 101? How? (c) In part (a) what is the largest number of caramels that Brenda can take, assuming you play your strategy guaranteeing the peppermint patty?
5. Divide and conquer. You're again facing your friend, Brenda, in a "candy-off” game involving a pile of 100 caramels and the winner's prize: one peppermint patty. (Like before, you still LOVE peppermint patties!). On their turn, each player can remove a
Transcribed Image Text:5. Divide and conquer. You're again facing your friend, Brenda, in a "candy-off” game involving a pile of 100 caramels and the winner's prize: one peppermint patty. (Like before, you still LOVE peppermint patties!). On their turn, each player can remove a
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