Question

Matt goes to purchase some electronics with gift cards issued in $15 and $55 dollar amounts. He is concerned that what he is purchasing does not maximize the value of his gift cards based on total cost of the electronics. Prove using strong induction that any total purchase of electronics that is $95.01 or higher will result in an unused gift card of maximum $4.99.

Answer 1

Strong induction is a type of proof closely related to simple induction. As in simple induction, we have a statement P(n) about the whole number n, and we want to prove that P(n) is true for every value of n.The difference between weak induction and strong indcution only appears in induction hypothesis. In weak induction, we only assume that particular statement holds at k-th step, while in strong induction, we assume that the particular statment holds at all the steps from the base case to k-th step

As he purchase for 95 .01 then the maximum will be 55 dollor and the other gift card will be useless