Puzzles for Programmers and Pros

5.3. No Change for the Holidays

Have you ever noticed that if a teenager is given $50 to buy a $20 item, no money comes back? Some other item was just so essential...

In this puzzle, we provide the teenager with a good excuse. Artiste and street vendor Claude sells beautiful handmade items for $100 or less but refuses to give change.

You have no cash, but you have three checks. You will make them out to Claude in whole dollar amounts. Your teenager is to give Claude the combination of checks that is the minimum amount more than necessary for the purchase price. For example, if you give your child a $50 check, a $30 check, and a $20 check and the item costs $53, your child will give Claude the $50 and $20 checks and Claude will keep the $17 in change in addition to the purchase price.

You like Claude's stuff, but you very much begrudge him his "I keep the change" attitude. So you'd like to minimize the amount he keeps beyond the purchase price.

5.3.1. Warm-Up

If you knew that the item in question cost either $20, $40, $50, or $60, which combination of three check amounts could you give in order to leave no change for Claude?

5.3.2. Solution to Warm-Up

$20, $40, and $50 is one among many solutions. Claude will not be able to keep anything in change.

1. If you did not know how much ...