Below the Sudoku board you will find discussions about the techniques used to solve this Sudoku. Use the buttons to the right and left of the board to step through.
Techniques used in this Sudoku:
Box Row Column
Triangulation
Obvious Singles
Last Free Cell
This is the strategy we will use:
We start with Box Row Column and Triangulation.
No solutions? Look for Obvious Singles and Last Free Cell.
No solutions? Go back to step 1.
There are 1s in boxes 4 (D4) and 5 (F8).
Box 3 needs a 1 and it has to be in row E, if we're lucky there will only be one cell available.
Only E1 is available! This is the Box Row Column technique:
If two boxes in a row or column have a repeated number, there may be only one option for the number in the third box.
Sometimes we are not so lucky. For example, we have 1s in cells E1 and I3. But in box 1, we have two cells (A2 and B2) that could contain the number 1. Let's keep searching...
There are 1s in C5 and D4. In this case the Box Row Column technique will need some help from the Triangulation technique. The 1 in I3 leaves only one free cell.
When Box Row Column leaves us with more than one option, Triangulation might help.
Triangulation:
The intersection of two or more values leaves only one option.
Box Row Column:
1s in G6 and I3.
1 in H9.
Box Row Column:
1s in F8 and H9.
1 in B7.
Box Row Column:
2s in E3 and F7.
2 in D6.
Box Row Column & Triangulation:
2s in G8, I4 and E3.
2 in H2.
Box Row Column & Triangulation:
2s in A5, C9, E3 and H2.
2 in B1.
Box Row Column & Triangulation:
3s in C7, D5 and I9.
3 in E8.
Box Row Column & Triangulation:
3s in F2, H4 and I9.
3 in G1.
We can't find 4s, 5s, or 6s with the Box Row Column technique, so we try 6.
Box Row Column & Triangulation:
6s in A8, E2, F5 and G9.
6 in D7.
We can't find 7s, or 8s with the Box Row Column technique, so we try 9.
Box Row Column:
9s in H6 and I2.
9 in G7.
We were able to fill a lot of cells! Now that we have more numbers, we can try again with 1.
Box Row Column & Triangulation:
1s in B7, E1 and I3.
1 in A2.
We can't find 2s, 3s, 4s, 5s, 6s or 7s with the Box Row Column technique, so we try 8.
8s in A9 and H7.
8 in D8.
Box Row Column & Triangulation:
8s in I1, C2, and D8.
8 in F3.
Box Row Column & Triangulation:
8s in D8, F3 and G4.
8 in E6.
Box Row Column:
8s in G4 and E6.
8 in B5.
No more options for the Box Row Column technique. We should now look for rows, columns or boxes with only one free cell. If none are found, as in this case, we look for those with two free cells.
Box 4 has two free cells and the missing numbers are 5 and 9. Since we have 5 in G3, 9 is the only option for cell D3.
This is the Obvious Singles technique:
There is only one possible solution for a cell.
So we write 9 in cell D3.
Only one free cell in box 4. So 5 goes to cell F1. This is the Last Free Cell technique:
If you have a single free cell in a row, column, or box, there's only one option.
Back to Box Row Column technique!
5s in F1 and G3.
5 in B2.
Last Free Cell in G2
When you see a last free cell, enter the number!
Last Free Cell in H3
Last Free Cell in D9
Back to Box Row Column technique!
5 in in C6
Box Row Column:
6s in G9 and H3.
6 in I6.
Last Free Cell in H5
Last Free Cell in G5
No more Last Free Cell, back to Box Row Column technique!
4 in I7.
Last Free Cell in I8
Last Free Cell in B8
Last Free Cell in C1
Last Free Cell in B9
Last Free Cell in E7
No more Last Free Cell, back to Box Row Column technique!
7 in A6.
Box Row Column:
3 in B6.
Triangulation:
3 in A3.
Last Free Cell in B3
No more Last Free Cell, back to Box Row Column technique!