Advent of Code 2015 - Day 17: No Such Thing as Too Much

Part 1

Description

The elves bought too much eggnog again - 150 liters this time. To fit it all into your refrigerator, you'll need to move it into smaller containers. You take an inventory of the capacities of the available containers.
For example, suppose you have containers of size 20, 15, 10, 5, and 5 liters. If you need to store 25 liters, there are four ways to do it:

• 15 and 10
• 20 and 5 (the first 5)
• 20 and 5 (the second 5)
• 15, 5, and 5

Filling all containers entirely, how many different combinations of containers can exactly fit all 150 liters of eggnog?

Input

Solution

For this problem, I decided to put all possible combinations and filtered them out. And, since there are 20 containers (my input), there are 2^20 = 1048576 possible combinations. Here is my Excel sheet:

I put this formula in AO1:

=SUMPRODUCT(U1:AN1,A$3:T$3)

and the similar formula for the rest of the cells. For solution, I counted only cells with sum of 150.

Part 2

Description

While playing with all the containers in the kitchen, another load of eggnog arrives! The shipping and receiving department is requesting as many containers as you can spare.
Find the minimum number of containers that can exactly fit all 150 liters of eggnog. How many different ways can you fill that number of containers and still hold exactly 150 litres?
In the example above, the minimum number of containers was two. There were three ways to use that many containers, and so the answer there would be 3.

Solution

To find the solution for part 2, I put this formula in AP1:

=IF(AO1=150,SUM(U1:AN1),"")

and count the smallest number among them using:

=SMALL(AP:AP,1)

and finally, another formula to find how many times it appeared:

=COUNTIF(AP:AP,4)