How many different sums of money can you make with three coins of different denominations?

Question

Thanks

Answer 1

It would depend on the denominations.
If the denominations are coprime with each other, then the number of different sums would equal to the power set of the coins.
If |A|=3, |Power set (A)|=2^3.
That includes the amount $0, i.e. no coin used.

A notable example would be for denominations
$0.10, $0.20, $0.40
would give all amounts from $0 to 0.70, giving 2^3=8 different amounts.

However, if a denomination is the sum of the other two, then the number of different sums will be reduced.
Try for example $0.05, $0.10, $0.20.