you have an infinite supply of coins of denomination 50p, 25p, 10p, 5p and 1p. In how many ways can you generate change for a

Question

Suppose you have an infinite supply of coins of denomination 50p, 25p, 10p, 5p and 1p. In how many ways can you generate change for a given amount, say for 100p?

Answer 1

Here's a path you can take:
1. Read this: https://brilliant.org/wiki/linear-diophantine-equations-one-equation/
2. Solve for 2 variables
3. Reduce n variables to n-1, continue until you reach 2 and work your way up
4. You're done. Celebrate!