Solving Sudoku - More Advanced Strategies

Sudoku puzzles can be complex, so it makes sense that there are numerous strategies for solving the puzzles.  As the difficulty level increases, the strategies change.  Here are more advanced strategies to help you wade through the sea of sudoku.

• Y-Wing Chains – Here is yet another example of how strategies build on each other to form new strategies. Y-Wing chains are an extension of the Y-Wing strategy.  A Y-Wing chain is a Y-Wing that has a locked pair.
• A locked pair actually has three sets of numbers, not two.  The first square is connected to the last square by one in the middle.  Example: The fifth and seventh squares of the ninth column both contain 4 and 6, as does the eighth square of the eight column.  The two squares in the ninth column are paired by being in the same column.  The seventh square of the ninth column and the eighth square of the eighth column are paired by being in the same block.  This means that the fifth square in the ninth column is connected to the eighth square in the eighth column through the seventh square in the ninth column. 
• To make the locked pair example a Y-Wing chain, add in the fifth square in the first column has 4 and 9, while the eighth square in the second column has 6 and 9.  The common number for these two square, which is 9, can be removed from any square that they both can see.
• XY-Chains – XY-chains build from the Y-Wing chain.  The setup of an XY-chain is the same as the Y-Wing chain, with one exception.  In a Y-Wing chain, the hinge of the chain is the locked pair, three squares containing the same two possible candidates.  In an XY-chain, the squares are not required to have the same two possible candidates.  Instead, there must be a common value.  Example: In an XY-chain with four squares, the squares could have 5 and 8, 3 and 8, 3 and 7, 7 and 5.  The 8 in the first connects to the 8 in the second, while the 3 in the second connects to the 3 in the third.  In this case, the square with 5 and 8 is one end of the chain, while the square with 7 and 5 is the other end.  This means that 5 can be removed as a candidate for all squares that the chain ends can both see.
• Aligned Pair Exclusion – The Aligned Pair Exclusion (APE) can be used to solve an XY-Wing, although an XY-Wing will not solve APE.  The basic rule of APE is that any two squares in the same row or column, that are also in the same block, cannot duplicate the contents of any square with two candidates that both squares can see.  Here is the logic: In the first square of a block, you have 4, 6 and 8 as candidates.  In a third square of the same block, you have 4 and 7.  A third square in the same row has 4 and 8, while a fourth has 7 and 8.  Your first two squares offer the possible pairs of 4/4, 4/7, 6/4, 6/7, 8/4 and 8/7.  If you use the pair 8/4, then you eliminate all candidates for one square in that row, while the pair 8/7 eliminates all candidates for another square.  You can eliminate those pairs as an option, along with 4/4, which is against the rules.  That brings you down to 4/7, 6/4, and 6/7.

These strategies, when combined with other basic and advanced strategies, can carry you through advanced sudoku puzzles.  While the puzzles will still take time, they can be fun instead of frustrating because you know how to solve them.