156849

Group 1 = 15, 20
Group 2 = 10, 5, 14, 6
Group 3 = 16, 19
Group 4 = 12, 8, 3, 2, 9, 1
Group 5 = 7, 11, 17
Group 6 = 13, 4, 18

To work this out:
- I first had to find out the the sum of numbers 1-20, which was 210
- I then had to divide this by 6 because there are 6 groups which was 35
- Next, I started to add numbers together to make 35.
- My method was to find a simple group with 2 numbers, then I found more numbers that added to 35, going through a process of elimination, until I had 6 full groups, with no numbers left.

It was mostly trial and error. I would be interested if there was another way.