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The two square - three line strategy for Sudoku puzzle solving

Explanation and discussion of perhaps the most useful and widely used solution strategy.

Two out of three lines [Game solving Strategies forum]

The two lines out of three lines strategy is one of the most useful Sudoku strategies. It finds most of the simplest to solve squares and can be used in a systematic manner to clear up the first and last few squares in the puzzle.

Take three lines (rows or columns) in a region. Look for the occurrences of a particular symbol, lets say '5' in these lines. If you find three occurrences then the symbol is 'solved' in those lines so move on to the next set of three. However if you find two then that automatically narrows down where the remaining '5' can occur, it can not occur in the two lines you have found containing the '5' or the regions of three squares in which the '5' occurs. You have narrowed the search so '5' must be in one of three squares. It's often the case that one or two of these squares are already filled so you can work out simply in which square the '5' must go. If you do this for each group of three rows then all groups of three columns you soon scan the whole grid for one symbol and then simply repeat for each symbol.

You can solve some of the 'easy' puzzles just by following this technique.

There is also a step-by-step guide to this technique here.

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One out of three (re: Two out of three lines) contributed by Alexander

You can often get so caught up in scanning for two occurrences in the three lines that you can ignore some other useful cases. If you find only one occurrence there are occasions when this is good too. Not quite so commonly, you can deduce that the symbol '4' say must occur in both of the remaining lines (row or column). However if one of the regions already has three sudoku squares filled in that forces the choice down to one group of three squares and an allocation can often be made.

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Useful tip (re: Two out of three lines)

I agree that it is a very useful sudoku technique.

It finds a lot of the cases where an allocation is forced because there is only one square in a group that a number can go.

However it won't find squares that have only one possible number to go in them and this is often necessary in solving puzzles.

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Dont miss out (re: Two out of three lines) contributed by John Wood

I've wasted lots of time by not using this tip consistently.

You have to have a system and when you use this technique make sure you have a standard scheme for looking for the two out of three strategy. I work through all the numbers 1 to 9, doing all rows and then all columns. You'll curse yourself if you miss out one or don't check it properly. If you solve a square go back and re-apply the strategy to the affected part of the grid, or if several solved just re-apply to the whole sudoku grid starting from scratch again.

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Super strategy (re: Two out of three lines) contributed by Huw

The two out of three is about the most important thing to learn about Sudoku.

The reason it works is that it makes easy to spot squares that can be solved using the only square sudoku rule. It is just a trick for finding squares that might be solved using this rule. It does not find out any squares that can be solved by the other strategies. It does not find all the squares that can be solved with the only square rule, so be careful!

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