X-Wing

Though this is difficult to put in words, I will attempt to explain it using an example image. In the image given below, for Row 1, the number 9 can be only in R1C2 or in R1C9. Similarly for Row 9 it can be in either R9C2 or in R9C9. I have circled these 4 cells and if you notice the intersecting lines making an X.


If 9 is in R1C2, then it gets eliminated from R9C2 and has to be in R9C9. Conversely, if 9 is in R1C9 then it is eliminated in R9C9 and has to be in R9C2. So the number 9 will always be on either end of one line of the X shape. and that takes care of number 9 for column 2 and Column 9. Hence for columns 2 and 9, the number 9 can be only in either Row1 or Row 9 and no where else. Hence 9 as a possibility can be eliminated from the cells in these two columns.(Highlighted in yellow)


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