Splitting $100

Due to Luc Longpre, as inspired by Dennis Shasha

Problem: You want to send someone to buy a gift at a store. The gift could cost anything up to $100. To pay for the gift, you write 3 checks. Your emissary can pay with some combination of the checks. Unfortunately, the store will not give change.

1. Assuming the price is in whole dollars and the check amounts are also whole dollars, what should the amounts be in order to minimize the worst case overpayment?
2. What should the check amounts be if the price is in dollars and cents and you write check amounts in dollars and cents?

Submitting solutions: Individual and team solutions should be emailed to Eric Freudenthal by midday on Thursday, 14 February with a subject line puzzle solution. All solutions should include a full list of collaborators and their email addresses .