What are the change combinations to make thirty one cents?

Answer 1

I'm going to list them all in sets of (Q, D, N, P), where Q = quarters, D = dimes, N = nickels, and P = pennies.

(1, 0, 1, 1)

(1, 0, 0, 6)

(0, 3, 0, 1)

(0, 2, 2, 1)

(0, 2, 1, 6)

(0, 2, 0, 11)

(0, 1, 4, 1)

(0, 1, 3, 6)

(0, 1, 2, 11)

(0, 1, 1, 16)

(0, 1, 0, 21)

(0, 0, 6, 1)

(0, 0, 5, 6)

(0, 0, 4, 11)

(0, 0, 3, 16)

(0, 0, 2, 21)

(0, 0, 1, 26)

(0, 0, 0, 31)

Thus, there are 18 total combinations.