gistfile1.txt

Instructions
To try and encourage more sales of different books from a popular 5 book series, a bookshop has decided to offer discounts on multiple book purchases.

One copy of any of the five books costs $8.

If, however, you buy two different books, you get a 5% discount on those two books.

If you buy 3 different books, you get a 10% discount.

If you buy 4 different books, you get a 20% discount.

If you buy all 5, you get a 25% discount.

Note that if you buy four books, of which 3 are different titles, you get a 10% discount on the 3 that form part of a set, but the fourth book still costs $8.

Your mission is to write code to calculate the price of any conceivable shopping basket (containing only books of the same series), giving as big a discount as possible.

For example, how much does this basket of books cost?

2 copies of the first book
2 copies of the second book
2 copies of the third book
1 copy of the fourth book
1 copy of the fifth book
One way of grouping these 8 books is:

1 group of 5 (1st, 2nd,3rd, 4th, 5th)
1 group of 3 (1st, 2nd, 3rd)
This would give a total of:

5 books at a 25% discount
3 books at a 10% discount
Resulting in:

5 × (100% - 25%) × $8 = 5 × $6.00 = $30.00, plus
3 × (100% - 10%) × $8 = 3 × $7.20 = $21.60
Which equals $51.60.

However, a different way to group these 8 books is:

1 group of 4 books (1st, 2nd, 3rd, 4th)
1 group of 4 books (1st, 2nd, 3rd, 5th)
This would give a total of:

4 books at a 20% discount
4 books at a 20% discount
Resulting in:

4 × (100% - 20%) × $8 = 4 × $6.40 = $25.60, plus
4 × (100% - 20%) × $8 = 4 × $6.40 = $25.60
Which equals $51.20.

And $51.20 is the price with the biggest discount.