# Sudoku difference between x wing and double pair

Double Pairs and X Wing are listed as different techniques here (former is a medium and later a master technique). The only difference I can see is double pairs are restricted to two neighbor blocks and x wing doesn't have that restriction. Is this the only difference or am I missing something else?

The x wing also looks like it needs to have pairs of possibilities in the corner cells. Is this always the case or can you use the x wing if 1+ corner(s) have more than the normal 2 possibilities?

The example of double-pair on that site unfortunately has the four relevant cells arranged in a rectangle, so it does rather make it look like an X-wing. It is really just a special case of their multi-line technique.

The way I spot the multi-line case is not by seeing the two lines they highlight in their explanation, but by spotting the other line going through the three blocks. This line has all its candidates for a digit in one block, therefore that block can't have that digit anywhere else.

Their explanation of X-wing is also somewhat confusing. It has nothing to do with pairs, like their example seems to imply. The point is that there are two lines that have the candidates for a particular digit in the same two locations (i.e. forming a rectangle). Any other candidates in those four cells are irrelevant. The other two lines that cross through those locations then cannot have that digit anywhere else. In their swordfish explanation they show you that x-wing is the 2-line equivalent of the 3-line swordfish. However, their explanation of swordfish also goes on about pairs of cells, which is a special case. Swordfish is merely 3 lines that have the candidates for a particular digit in the same three locations (or in just two of those three locations).

There is a neat relationship between the some techniques, which is not particularly useful unless you are writing a computer program, but it may be of interest anyway.

Imagine you have 9 sudoku grids stacked on top of one another, forming a 9x9x9 cube. Each layer represents a digit. Instead of writing a digit in a cell on the original sudoku grid, you merely colour in that cell in the layer for that digit in this sudoku cube.

A solved sudoku then corresponds to a cube with 81 coloured cells, and along each of the three axes there is exactly one coloured cell in each line.

The single position technique in a row or column means that in this sudoku cube there is only one cell left in a line along the x- or y-axis that can be filled. The same thing in a line along the z-axis is the single candidate technique. So single position and single candidate are really equivalent techniques.

In the same way naked pairs, hidden pairs, and x-wing are essentially identical techniques on this sudoku cube, merely applied along different axis directions. Naked triples, hidden triples, and swordfish are similarly related.

Note however that any technique that specifically involves blocks, such as candidate line or multi-line, is not related to other techniques in this way. This is because the blocks only exist in one direction so the technique cannot be applied to the sudoku cube along a different direction.

The difference is that a double pair operates on two columns or rows of the same block column or row, i.e. if you know the left and middle columns of a block column are occupied by a digit, the other location of the digit must be in the right column, without knowing the precise locations of the left and middle digits.

An X-wing doesn't have this advantage, and is a lot harder to spot, although it's elimination of digits method is very much the same.