Strong Induction and Gift Card Totals
Suppose that a store offers gift certificates in denominations of 25 dollars and 40 dollars. Determine the possible total amounts (below $160) you can form using these gift certificates.
Prove your answer using strong induction.
https://brainmass.com/math/discrete-optimization/strong-induction-gift-card-totals-510423
Solution Preview
** Please see the attached file for the complete solution **
Proof. At first, the amounts seem semi-random. All possible combinations are:
$25 certificates $40 certificates Total
1 0 $25
0 1 $40
2 0 $50
1 1 $65
3 0 $75
0 2 $80
2 1 $90
4 0 ...
Solution Summary
This solution uses strong induction to find every possible total amount using a combination of gift card values.