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Singles in Rows, Columns, and Blocks Strategy

One strategy for solving a square in sudoku is to check if a square can only contain one specific number and no other numbers.

Singles in Row or Column

For example, let's say that you have the following puzzle:


...|...|...
...|...|...
...|...|...
---+---+---
...|...|...
.23|456|789
...|...|...
---+---+---
...|...|...
...|...|...
...|...|...

The first square in the example row is unsolved. However, you can tell what that square should be, because all of the other numbers are filled in. The empty square should be a 1.

Singles in Block


...|...|...
...|...|...
...|...|...
---+---+---
.23|...|...
456|...|...
789|...|...
---+---+---
...|...|...
...|...|...
...|...|...

The unsolved square in the block only has one possibility, because all of the other squares in that block are filled in. Because of that, the unsolved square has to be a 1.

A More Complicated Example

The above examples are very simplified. Here is an example that isn't as easy to solve.


.4.|...|...
...|...|...
.6.|...|...
---+---+---
3..|...|...
.?.|.5.|.7.
..2|...|...
---+---+---
.9.|...|...
...|...|...
.8.|...|...

Look at the square with the question mark. There is only one possible number that that question mark could be. What is it?

The block contains 2 and 3, so it can't be those. The column contains 4, 6, 9, and 8, so it can't be those. That leaves 1, 5, and 7 as possibilities. However, the row has a 5 and 7, so the only possible number for the question mark is 1.

Finding Singles

To find squares that have only one option like with the above examples, you have to find squares that are surrounded by at least eight numbers. The eight numbers can be in the same row, column, and block as the unsolved square. Check those surrounding numbers to see if there is only one number missing. If so, you have solved the square.

Example Puzzle

Try solving the following interactive puzzle. It can be solved using only the Singles in Rows, Columns, and Blocks strategy.

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