The rules are the same as the classic Sudoku, but the numbers outside the grid are the sum of the first three digits placed closest to that row or column
I think this should be the unique solution:
You have to start by finding missing numbers on the frame and the row/column sums for the middle 3x3 which are not given in the puzzle.
Intermediate steps (it's difficult to pen down all the minor steps as there is lot of elimination, pigeonholing):
- Solve upper left 3x3 by looking at possible combinations adding up to 12,11,22 and then 21,14,10.
Populate middle 3x3 as much as you can based on column and row sums
- Break the ties using the fact that some of the columns and rows in a 3x3 have the same sum
With some more effort, I got one solution:
I'm almost certain that this is the unique solution - not totally certain because my sketch is a bit chaotic and there could be error(s) in the deduction.
There is not so much to say about my method. As some comments suggest, it is very hard to solve without a computer, and I also used the help of a computer.
More specifically, I did everything in Photoshop. With the ability of creating layers and changing colors, I can easily go back to the last "guess point", as soon as a contradiction occurs.
The rest is just trial-and-error, plus some patience.