Assuming you're not used to staring at a full pencilmark grid, here's how to do it without them:
- Code: Select all
*-----------*
|...|1..|...|
|.1.|4.3|.85|
|7..|..2|19.|
|---+---+---|
|45.|3.1|.29|
|...|.2.|...|
|182|..4|.3.|
|---+---+---|
|.41|...|..2|
|62.|5.7|...|
|...|..8|...|
*-----------*
1) Look at row 9. Where can you place digit 2? There's only one possibility, r9c4, which is called hidden single. That brings you here:
- Code: Select all
*-----------*
|...|1..|...|
|.1.|4.3|.85|
|7..|..2|19.|
|---+---+---|
|45.|3..|.29|
|...|.2.|...|
|182|..4|.3.|
|---+---+---|
|.41|...|..2|
|62.|5.7|...|
|...|2.8|...|
*-----------*
2) Look at box 8 and row 7. In row 7, digits 1 and 4 are in columns 2 and 3. Which 2 cells do these digits have to occupy in box 8? That's right, r89c5. These two cells have to hold these digits, no other digits may go in those two cells (hidden pair). What's the remaining possibility for digit 3 in box 8?
Once you have figured that out, the next step is easiest described if I only show the essential information:
- Code: Select all
*-----------*
|.|.|...|...|
|-+-|4--|-85|
|7|.|...|...|
|---+---+---|
|.5.|...|...|
|.|.|...|...|
|.8.|...|...|
|---+---+---|
|.4.|...|...|
|...|...|...|
|...|...|...|
*-----------*
3) You already have digits 458 in both row 2 and column 2. In box 1, none of the cells in row 2 or column 2 may hold any of those three digits. This leaves only three possible cells for three digits, those three cells have to hold those three digits and no other digits may go in those three cells (hidden triplet). Knowing that r1c1, r1c3 and r3c3=458 and nothing else, what is the remaining possibility for digit 2 in box 1? When you've found out that, you can also solve the last digit 2 in box 3, which brings you here:
- Code: Select all
*-----------*
|...|1..|2..|
|21.|4.3|.85|
|7..|..2|19.|
|---+---+---|
|45.|3..|.29|
|...|.2.|...|
|182|..4|.3.|
|---+---+---|
|.41|.3.|..2|
|62.|5.7|...|
|...|2.8|...|
*-----------*
4) Remember step 1), r8c5 must be either 1 or 4. Then look at r8c8, what are the possibilities there? As both r8c5 and r8r8 must be either 1 or 4, it means that those two digits must be in those two cells, and may be in no other cells of the same row (naked pair). No solved digit yet, but remember this in the next step.
5) Look at box 3. Where can you place digit 3? As the 3 in box 3 has to be in either r1c9 or r3c9, digit 3 may be in no other cells of column 9 (locked candidates).
6) Now, what digit could be in r8c9? It can already see digits 2,5,6,7,9 and cannot be any of these. It cannot be 1 or 4 (step 4), it cannnot be 3 (step 5). Only remaining possibility is 8 (naked single). That also gives you the location of the 8 in box 7, leading here:
- Code: Select all
*-----------*
|...|1..|2..|
|21.|4.3|.85|
|7..|..2|19.|
|---+---+---|
|45.|3..|.29|
|...|.2.|...|
|182|..4|.3.|
|---+---+---|
|841|.3.|..2|
|62.|5.7|..8|
|...|2.8|...|
*-----------*
7) Remember step 3). r1c1 must be either 4, 5 or 8, but now you already have 4 and 8 in the column, leaving only one possibility.
The rest of the puzzle is easy, even without pencilmarks.
RW