How many ways can you make change: Some easy proofs
History and Overview
2014-07-22 v5 Combinatorics
Abstract
Given a dollar, how many ways are there to make change using pennies, nickels, dimes, and quarters? What if you are given a different amount of money? What if you use different coin denominations? This is a well known problem and formulas are known. We present simpler proofs in several cases. We use recurrences to derive formulas if the coin denominations are {1,x,kx,rx}, and we use a simple proof using generating functions to derive a formula for any coin set.
Cite
@article{arxiv.1406.5213,
title = {How many ways can you make change: Some easy proofs},
author = {William Gasarch},
journal= {arXiv preprint arXiv:1406.5213},
year = {2014}
}