Java Algorithm to solve vendor machine 'change giving' problem

Question

As a graduate I went for an interview for a java development role and was doing pretty well in the technical examinations until i came up against this question.

If i

Answer 1

Let say your possible coins are x1 ...xn :

if you're asked to print all the possiblities for $2 then you could print recursively all the possibilities for :

2-x1
2-x2
..
2-xn

Yoou will eventually get all the solutions

You can initialise this recursive process with amount-xi = 0 then print