I think this should be the unique solution:

You have start by finding missing numbers on the frame and the row/column sums for the middle 3x3 which are given in the puzzle.

Intermediate steps (it's difficult to pen down all the minor steps as there is lot of elimination, pigeonholing):

1. Solve upper right 3x3 by looking at possible combinations adding upto 12,11,22 and then 21,14,10.

2. Upper middle 3x3 has rows adding to 19, 19, 7; 7 can only come from 1,4,3; possible combinations for 19 are 9,7,3 and 8,6,5

3. Populate middle 3x3 as much as you can based on column and row sums

4. Break the ties using the fact that some of the columns and rows in a 3x3 have the same sum

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):

1. Solve upper left 3x3 by looking at possible combinations adding up to 12,11,22 and then 21,14,10.

2. Upper middle 3x3 has rows adding to 19, 19, 7; 7 can only come from 1,4,3; possible combinations for 19 are 9,7,3 and 8,6,5

3. Populate middle 3x3 as much as you can based on column and row sums

4. Break the ties using the fact that some of the columns and rows in a 3x3 have the same sum

I think the should be the unique solution:

You have start by finding missing numbers on the frame and the row/column sums for the middle 3x3 which are given in the puzzle.

I think this should be the unique solution:

You have start by finding missing numbers on the frame and the row/column sums for the middle 3x3 which are given in the puzzle.

Intermediate steps (it's difficult to pen down all the minor steps as there is lot of elimination, pigeonholing):

1. Solve upper right 3x3 by looking at possible combinations adding upto 12,11,22 and then 21,14,10.

2. Upper middle 3x3 has rows adding to 19, 19, 7; 7 can only come from 1,4,3; possible combinations for 19 are 9,7,3 and 8,6,5

3. Populate middle 3x3 as much as you can based on column and row sums

4. Break the ties using the fact that some of the columns and rows in a 3x3 have the same sum