If you stay with positive non-zero integers without decimals, you can't sum up 6 totally different numbers to get 20. The first 6 whole numbers, (1, 2, 3, 4, 5, 6) sum to 21, and there's really no other way of getting smaller than that without including decimals or negatives, or zero as one of the numbers.
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I answered this someplace else, but on a standard dartboard it's all the numbers 1-20 (so 20 total)
You can choose 3 objects from 6 20 ways, assuming order does not matter
The sum of the first six numbers is (6 x 19) = 114The sum of the new group of seven numbers is (7 x 20) = 140The seventh number is (140 - 114) = 26.==========================================The seventh number contains enough material to make itself 20and also to raise each of the previous six numbers from 19 to 20.Therefore it must be [ 20 + (6 x 1) ] = (20 + 6) = 26.
7 different numbers.35711131719
20