How do you feel about your progress as a sudoku solver? By now, you should be picking up most puzzles without fear but there are plenty more sudoku tips to learn before we are finished with this subject. In theory, the subject for this post should be hidden triples and quads. I will confess to finding them a bit boring, so I have jumped on a bit. Think of them in exactly the same way as a hidden pair is related to a naked pair and you should get the idea very quickly. If anyone is desperate to see them in action, let me know and I will do another quick post.
Anyway, the subject for today is one close to the hearts of Star Wars fans the world over. This technique is called the X-Wing and you will see why as we look at an example. Study rows 2 and 7 in the image below.
Did anything stand out for you?
If you go back to the diagram and check out the cells where 5 is a candidate, you should find that they only exist in columns 2 and 5 in both rows. That is, there are no other candidate 5’s anywhere else in those rows and the ones we have just happen to line up to make a kind of rectangle.
What happens in this situation is a similar kind of effect to the one we saw with naked pairs. Because there are no other candidate 5’s in the first of the two rows, when we imagine that the leftmost 5 IS correct, the other one cannot be 5….and because any 5’s in the same column also get cancelled out, that means the righthand 5 in the lower row must also be correct. In the same way, if we chose the righthand 5 in the upper row, then it must mean that the lefthand 5 is correct in the lower row.
This gives us a kind of “cross” of possibilities and if I highlight both at the same time, we have the X-Wing shape.
In the example case, this helps us because we know that the two 5’s must exist in one or other of those variations and so it can’t stray out any further into the column. Imagine that another 5 in column 2 is correct, in that case both of the candidates in rows 2 and 7 would be wrong and so both 5’s for those rows must be in column 5 together – and that’s not allowed in this particular universe!!
What we have learned in this case, is that there can be no other candidate 5’s in either of our two columns and so we can cancel them out and look for new progress. Bear in mind that after using a more advanced technique like this, you should look back to earlier techniques as other possibilities may have been revealed.
So, to summarize, you start this by looking for a “rectangle” of identical candidates (all 1’s, all 2’s etc.) and then you see if they are alone in their respective rows or columns. If they are, you have found an X-Wing and you can look for candidates to cancel. Remember, if the X is clear in the rows, you cancel in the columns and vice versa.
More tips on how to play sudoku next time.