Swordfish

A while ago I explained the X-Wing solving technique.
Recently I shown my explanation of other basic, Classic Sudoku solving techniques.

The only remaining solving method that I don’t consider trial and error is Swordfish. So, to complete the list of Sudoku solving tips, here is an example of a Sudoku puzzle that can be solved using Swordfish.

Here is the puzzle:

This is how far you can get without using Swordfish:

After you pencil-in all the numbers, you focus on number 4 and you look at columns 1, 5 and 7. In those 3 columns, number 4 appears altogether in precisely 3 rows: 1, 7 and 8. So, 3 columns with candidates in only 3 rows, it follows that (since each number can appear only once in each column and each row) number 4 can be eliminated from rows 1, 7 and 8 except from those cells that belong to columns 1, 5, 7. In other words, number 4 appears in precisely 3 cells from those 7 that I highlighted with a red rectangle. Of course, those 3 cells must be in different columns/rows, but the point is that in rows 1, 7 and 8 number 4 cannot appear in any other cell.

This indirectly solves R1C8 – because it can’t be 4 the only other option is 7.

I hope this makes sense.

Download the final solution.
Download the text file to import to Perfect Sudoku.