Question

how many ways can you make a dollar using only nickels quarters and half dollars

Answer 1

You can solve it by brutal force:

(50,50)
(50,25,25)
(50,25,5,5,5,5,5)
(50,5,5,5,5,5,5,5,5,5,5)
(25,25,25,25)
(25,25,25,5,5,5,5,5)
(25,25,5,5,5,5,5,5,5,5,5,5)
(25,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5)
(5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5)