Teach Yourself How to Play Sudoku: Lesson #10: SHARED PAIRS

Teach Yourself Sudoku

Learn the secrets that let you easily solve Sudoku puzzles faster!

Lesson #10. Pick a Pair of SHARED PAIRS

Let me preface this section by saying that in my experience, having to use the logic of SHARED PAIRS to solve a Sudoku puzzle is a rare event. After playing close to a thousand Sudoku difficult puzzles, I bet I’ve used it on less that a handful of occasions. But it is a useful technique and can be absolutely necessary to solve a difficult puzzle so it’s worth knowing about.

Let’s start by looking at the Sudoku puzzle fragment below:

There are lots of POSSIBLES here but a quick scan will reveal that we have a TEAM of 2 in both the left and right Blocks (7,8 and 1,7 respectively.) Also, both of the TEAMS share the same Rows (1 and 3). And, finally, the TEAMS have the number 7 in common. I’ve circled the relevant cells to make it easier for you to see this pattern.

OK, so what? Well, we can actually use the facts (TEAMS of 2 sharing the same Rows and having a number in common) to solve a part of the puzzle. Here’s how.

Let’s go clockwise around the grid segment starting in the upper right and play “What if?” by trying different numbers in different cells and seeing what the implications are. To start, let’s pretend that the (7,8) cell in Row 1 is really a 7. If that’s true then the (1,7) cell at the other end of Row 1 must be a 1, and the (1,7) below that in Row 3 must be a 7, and bringing us back to the left Block, the (7,8) in Row 3 must be an 8. Here’s how the grid would look. (If you’re confused, go back to the previous grid fragment and compare it to this one.)

Now, let’s take the other option. What if we said that the first (7,8) was really an 8 instead of a 7? Look at how things would resolve then.

Now, at this point time, we don’t know which of these scenarios is actually the solution but we can make one useful observation. In either case, the 7s that belong in Rows 1 and 3 will be in the left and right Blocks but NOT in the center Block (this is because the PAIRS SHARE a 7 and it must be placed in one or the other location.) Therefore, we can erase all of the 7s in Rows 1 and 3 in the center Block which leaves us with this grid:

Now, look closely at the remaining POSSIBLES in the center Block.

You’ll see that we’ve uncovered an ONLY ONCE in the center Cell and it’s a 7 which we can then write in thusly.

So although we couldn’t resolve any of the original pairs (the 7,8 or the 1,7), we were able to use them to determine the contents of another cell.

Here are the things you should be looking for if you’d like to take advantage of SHARED PAIR logic to solve your Sudoku puzzles:

- a PAIR of TEAMS of 2

- occupying the same Rows

- having a SHARED number in common

If you identify this pattern in a Sudoku puzzle, you can then confidently erase the SHARED number from the Rows or Columns in the other Block (“other Block” means the Block that doesn’t contain either of the PAIRS.)

In the example shown here, we were able to eliminate all but one of the 7s in the center Block leaving an ONLY ONCE in the center Cell and thus solving that Cell. You may not always be able to solve another Cell immediately using the SHARED PAIR technique but it can reduce the number of POSSIBLES in the other Block and you’ll be that much closer to solving the puzzle.

NOTE: Theoretically, you could use the logic of the SHARED PAIR technique and expand it so that it applies to TEAMS of 3 or 4 or more (remember that our example used TEAMS of 2.) In those cases you’d have 3 or 4 or more cells per Block involved and they would have to occupy the same Rows / Columns and there would have to be a number that was shared in common. As a practical matter, this pattern is more difficult to identify due to the complexity of the situation and I’ve never run across a case of it in the wild but FYI, it is possible. If you run across one, the same logic would apply: Go ahead and erase the SHARED number from the Rows / Columns in the other Block.

NEXT UP: Lesson #11. What if?