# Puzzle of the day, Frame Sudoku

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 feel this will be super tough without a computer. Commented Apr 13, 2020 at 19:15
• @Jonathan Look at this OP's previous puzzles: they're super tough, but usually doable, without computers. Commented Apr 13, 2020 at 19:18
• I've double-checked all my steps and I can't find where I made a mistake :-/ but I seem to be getting a contradiction. Maybe it's just too late at night for this ... Commented Apr 13, 2020 at 20:36
• Isn't this just Killer with some cells left blank? And why are some of the perimeter cells blank when their value is obvious?
– JMP
Commented Apr 13, 2020 at 20:45
• @JMP How are their values obvious?
– Jens
Commented Apr 13, 2020 at 21:36

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.

1. 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

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

1. 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:

642793581
713856429
895241637
287165394
469328715
531479268
926517843
374982156
158634972

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.