Smallest bill stack covering change from 100
Question
Customers pay for purchases of any whole-dollar amount from $1 to $99 with a $100 note. You may hold $1, $5, $20 and $100 bills. What is the smallest number of bills you need so that you can always hand back exact change?
Short answer
11. The change ranges over $1 to $99, and $99 alone needs at least twenties, fives and ones, i.e. bills. That same set of bills can form every amount from $1 to $99 by taking a sub-collection, so suffices.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
Open the worked solutionLessons behind this question
- Conditional Probability, Total Probability, and Bayes' Rule
- Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating
Start with a free lesson: Probability Fundamentals is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.
Read it free