From Alonso del Arte, Oct 10 2017: (Start)
There are just three ways to partition 100 into its distinct divisors: 100 = 50 + 25 + 20 + 5 = 50 + 25 + 20 + 4 + 1 (see A033630).
However, it's not possible to exchange a United States 1-dollar coin for smaller coins of distinct denominations in current circulation since there are no 4- or 20-cent coins (see A112024).
Nor is it possible to exchange a 100-dollar bill for smaller bills of distinct denominations as there are no 4- or 25-dollar bills (see A124146). (End)