Book Store

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%) x $8=5\times 8\; =\; 5\; \times$6.00 = $30.00, plus
• 3 × (100% - 10%) x $8=3\times 8\; =\; 3\; \times$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%) x $8=4\times 8\; =\; 4\; \times$6.40 = $25.60, plus
• 4 × (100% - 20%) x $8=4\times 8\; =\; 4\; \times$6.40 = $25.60

Which equals $51.20.

And $51.20 is the price with the biggest discount.