What Is the Minimum Amount of Money Needed with Different Coin Combinations?

[mamma_mia66]

Homework Statement

use combinatorial methods to determine the smallest amount of money that using cents, nickels, dimes, or quarters, requires
a) four coins
b) five coins
c) six coins
d) seven coins
e) eight coins

Hint: Consider the ways to partition sets of those respective sizes and calculate their minimum values.

Homework Equations

The Attempt at a Solution

a) four coins => 4 cents (1cent+1cent+1cent+1cent)

b) five coins => 9 cents (1nickel + 4 cents)

c) six coins => 19 cents (1 nickel + 1 dime + 4 cents)

I don't know how to do d) ans e)

I can't use 5 cents , because this is makes 1 nickel.

Please help. Thank you.

 

[mutton]

I can't use 5 cents , because this is makes 1 nickel.

By similar reasoning:
You can't use 2 nickels because they make 1 dime.
You can't use 2 dimes and 1 nickel because they make 1 quarter.
These restrictions help you pick the next coin, but the question requires the use of combinatorial methods.