X-Wing Technique is an advanced technique in Candidates Elimination Techniques. It is less used but it can effectively reduce the number of candidates when applied. The following example can help you gain a better understanding of this technique:
In Row B and Row G, candidate 7 occurs and only occurs at 2 possible locations, which are in Column 2 and Column 7 respecitively. In other words, in Row B and Row G, value 7 should be assigned either to cells in Column 2 or to cells in Column 7.
Suppose if [B2] = 7, then [G2] cannot be assigned 7 since these two cells are in the same column. Therefore, for Row G, [G7] must be assigned 7. Otherwise, there will be no 7 in Row G.
Or suppose if [B7] = 7, then [G7] cannot be assigned 7. And value 7 can be placed only to [G2] in Row G.
In Simple words, there are only two cases for Row B and Row G:
No matter which result will actually happen, value 7 must exist in Column 2 and Column 7, so that other cells in these two columns cannot hold candidate 7. Therefore, we can safely remove 7 from those cells. In this example, value 7 will be removed from [A2] of Column 2, and from [C7], [D7] and [E7] of Column 7.
In summary, if a number has only two locations in two different rows and these locations happen to lie in the same two columns, then this number can be removed from the candidates of other cells of these two columns.
Similarly, if a number has only two locations in two different columns and these locations happen to lie in the same two rows, then this number can be removed from the candidates of the other cells of these two rows. See the following example:
We can see that in Column 1 and Column 7, value 9 can only be found in Rows C and G, so we can use X-Wing Technique to safely remove 9 from [C4] and [C5] in Row C and from [G2] and [G5] in Row G.
You can never find X-Wing in blocks.
See Also:
