You'll still have to somehow determine the correct order, but knowing exactly which digits appear in that row is a great start.


Triangular numbers: 3 in 2 cells, 6 in 3, 10 in 4, 15 in 5, 21 in 6, 28 in 7, 36 in 8, and 45 in 9.
Triangular numbers plus one: 4 in 2, 7 in 3, 11 in 4, 16 in 5, 22 in 6, 29 in 7, and 37 in 8.
45 minus triangular numbers: 45 in 9, 44 in 8, 42 in 7, 39 in 6, 35 in 5, 30 in 4, 24 in 3, and 17 in 2
44 minus triangular numbers: 43 in 8, 41 in 7, 38 in 6, 34 in 5, 29 in 4, 23 in 3, and 16 in 2.;
, For example, suppose a 23 in 3 intersects a 28 in 7. The 23 in 3 can only be 6 + 8 + 9. The 28 in 7 can only be 1 + 2 + 3 + 4 + 5 + 6 + 7. The only digit in common is a 6, so that must be in the intersection.
 The triangular numbers are again critical for this step. For example, there are several ways to get 27 in 4, but none of them can use a 1 or a 2 (since the maximum for the other 3 digits is 7 + 8 + 9 = 24) and all need a 9 (since 5 + 6 + 7 + 8 = 26).
 For example, if the above 27 in 4 crossed a 7 in 3, we could conclude that the cell in the intersection contained a 4. That also implies that the 27 is 4 + 6 + 8 + 9.
, Although you might not be able to say much about a 20 in 5 initially, once you learn that that row contains a 9, then it looks like a 11 in 4 and therefore must be 20 = 1 + 2 + 3 + 5 + 9.
Look for rows or columns that can only be made with one combination of digits.
Look for cells that can only take one digit after considering both their row and column restrictions.
Find the maximum and minimum digits that could be in any row or column.
Compare these restrictions with those in the crossing rows.
If a row or column must contain a certain digit, look for where in that row or column it could go.

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Continually reevaluate these steps as you discover new information.
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