We need 3 numbers from the list that add up to 42, without duplicating any of the numbers within the group of 3.
Take the largest number 27 and subtract from 42, 42-27=15. The other two numbers must sum to 15. The list of such pairs is (14+1), (13+2), (12+3), (11+4), (10+5), (9+6), (8+7). (7 pairs)
Now take the second largest number 26 and subtract from 42, 42-26=16. So the pairs will be:
(15+1), (14+2), (13+3), (12+4), (11+5), (10+6), (9+7). (7 pairs)
Next is 25. Pairs to sum to 42-25=17:
(16+1), (15+2), (14+3), (13+4), (12+5), (11+6), (10+7), (9+8). (8 pairs)
Next: 24. Pairs to sum to 18:
(17+1), (16+2), (15+3), (14+4), (13+5), (12+6), (11+7), (10+8). (8 pairs)
Next: 23. Sum to 19:
(18+1), (17+2), (16+3), (15+4), (14+5), (13+6), (12+7), (11+8), (10+9). (9 pairs)
Next: 22. Sum to 20:
(19+1), (18+2), (17+3), (16+4), (15+5), (14+6), (13+7), (12+8), (11+9). (9 pairs)
Next: 21. Sum to 21 (this is the halfway point):
(20+1), (19+2), (18+3), (17+4), (16+5), (15+6), (14+7), (13+8), (12+9), (11+10). (10 pairs)
Next: 20. Sum to 22:
(19+3), (18+4), (17+5), (16+6), (15+7), (14+8), (13+9), (12+10). (8 pairs)
Next: 19. Sum to 23:
(18+5), (17+6), (16+7), (15+8), (14+9), (13+10), (12+11). (7 pairs)
Next: 18. Sum to 24:
(17+7), (16+8), (15+9), (14+10), (13+11). (5 pairs)
Next: 17. Sum to 25:
(16+9), (15+10), (14+11), (13+12). (4 pairs)
Next: 16. Sum to 26:
(15+11), (14+12). (2 pairs)
Last: 15. Sum to 27:
(14+13). (1 pair)
There are 85 sets of numbers 1-27 adding up to 42, with no repeat combinations or duplications within the combo.