If you were to have 6 unequal piles all with different amounts of cards to each other this would be impossible as the minimum number of cards you would need would be 21 (1+2+3+4+5+6=21). However, I have found a solution that uses 3 piles of 2, a pile of 5, a pile of 3 and a pile of 6. Firstly I added up all the values of the cards to give me a total of all the cards together. Then I divided this total by 6, as this is how many piles Katie arranged the cards into. This gave mean amount that was the target total for each of the piles of cards to each.
1+2+3+4+5+6+7+8+9+10=55 55+55=210 210/6=35 Target-366
11+12+13+14...+20=155
1st pile-20,15 2nd pile-16,19 3rd pile-17,18 4th pile-11,8,1,5,10
5th pile-14,12,9 6th pile-2,3,4,6,7,13