Money Combinations

Question

Please note that I have tried to the best of my ability everything but in my work I have to assume distinct possibilities which means that 5 pennies and 1 nickel are different amounts. I am lost.

Chance has quarters, dimes, and nickels. His mother makes him give 6 coins to his sister. How many different monetary values can he give his sister?

I don't understand how pennies even come into consideration. — Joffan, Jul 31 '16 at 06:04
It was an example I suppose and I wasn't thinking that well because it was 2 in the morning. No rush though. — Ian L, Jul 31 '16 at 17:25

score 0 · Answer 1 · answered Jul 31 '16 at 06:58

A nickel is 5 cents, a dime 10 and a quarter 25. All are multiples of 5, so we can divide 5 out and we'll get the same result:

I choose six times from {1, 2, 5} and sum up my choices. How many possible sums can I get?

This is easy enough to list.

Number of fives in selection f = 0: {1, 1, 1, 1, 1, 1} (Σ = 6), {2, 1, 1, 1, 1, 1} (7), … {2, 2, 2, 2, 2, 2} (12)
f = 1: {5, 1, 1, 1, 1, 1} (Σ = 10), …, {5, 2, 2, 2, 2, 2} (15)
f = 2: {5, 5, 1, 1, 1, 1} (14), …, {5, 5, 2, 2, 2, 2} (18)
…
f = 5: {5, 5, 5, 5, 5, 5} (30)

The possible sums fall in the ranges 6-12, 10-15, 14-18, 18-21, 22-24, 26-27 and 30. Combining, this gives the ranges 6-24, 26-27 and 30, and there are 22 possible sums (monetary values) in total. This is the answer.

Related to your query is A119651, which counts how many possible values n pennies/nickels/dimes/quarters can sum to.

Money Combinations

1 Answers1