Question on EPW for maths

three pigs brought back 7 mushrooms arrange the mushrooms in the baskets so any total of mushrooms from 1-7 can be made. u cannot remove any mushrooms from baskets to help make up the totals for this question.

- eg
1 mushrooms from basket 1
2 mushrooms from basket 2
3 mushrooms from basket 3
4 mushrooms from basket 1 and 3
5 mushrooms from basket 2 and 3
6 mushrooms from basket 1, 2 and 3

pigs discovered two things;
-- the total no of mushrooms collected was 6
-- by choosing different combination of baskets (and without taking any mushrooms out of their baskets) they could make any total of mushrooms from 1-6.

basket 1: 1 mushroom
Basket 2: 2 mushroom
basket 3: 4 mushroom

To get one mushroom, take the first basket
to get 2, take the second
to get 3, take the first and second
to get 4, take the 3rd
to get 5, take the 3rd and 1st
to get 6 take the third and 2nd
to get 7 take all 3 baskets


To work this out, just use trial and error (that's the easiest and quickest way, since you only have to make numbers up to 7.)

I have solved a problem similar to this before, except we had to make the numbers up to 20 something.

EDIT: Note these are all powers of 2, 2^0, 2^1 and 2^4. Just in case you need to talk about that in the assignment/question.