My local store sometimes runs offers on some of its products. There are three different types of offers that could be in place:

* Buy a certain number of a particular product and get an extra one for half price.

* A percentage discount (always a multiple of 5%) on one particular product.

* A percentage discount (always a multiple of 5%) on purchases worth a total of more than $10.

The store only ever has one of these offers in place at any time.

Last week I bought :

3 cartons of orange juice for $4 each

1 loaf of bread for $3

5 packets of snacks for $1 each.

This week I bought the same set of items, but only paid $18 even though the individual items still had the same price.

(a) (1) There are two possible offers that could be applied to orange juice that would each explain this reduction in the total bill.

What are these two offers?

(a)(2) What are the other two offers that could explain the reduction in the total bill? ...............

(b) In order to work out which offer is in place this week, I am going to make another purchase. What is the minimum that I must buy in order to be certain about which offer is in place?