156775

I just summed the whole numbers involved from 1 to 20, then I divided by 6 (the number of piles) which gives me 35. So each pile has to have numbers that summ in total 35, so I started to pick 20+15 in the first pile, then the second highest number 19 and then 35-19=16, so I picked 16 from the pool of the numbers and I continued in that way til all numbers are chosen without repeting none of them. i.e. the third highest number is 18, so 35-18=17, so for the third pile I chose 18 and 17 which gave us 35.