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# Solving Techniques 11 X-Cycles

Before considering X-Cycles, it’s important to understand strong links and weak links.

As shown below, a link where only two numbers are possible in a row, column or box, is called a strong link. In the diagram, it is between [1] and [2].

As shown below, a weak link is a link where there are more than three numbers that are possible within a row, column or box. [1] and [2] are in three possible cells, which creates a weak link.

## X-Cycles

The most simple X-cycle is shown in the diagram below. The red line is the strong link, the dotted red line, the weak link.

This works the same way as an X-wing and it always works out to:
1
1
or
1
1
Hence, 1 can’t be entered in the areas marked X.

So the X-cycle, of a given number, refers to a
cell - strong - cell - weak - cell - strong - cell
or
cell - strong - cell - weak - cell - strong - cell - weak - cell - strong - cell
type of loop that begins and ends with a strong link. (It also works, if there are strong links, instead of weak within the pattern.)
The number in the weak links can be removed as candidates, but these cells change depending on the situation.

## X-Cycles 2

This is a slightly complex pattern. The red line is a strong link, the dotted red line is a weak link.

Where the 1 goes is in one of the two patterns below.

Pattern A

Pattern B

Hence, in the overlapping areas X, 1 can’t be entered, as shown below.

## X-Cycles 3

Below is another complex pattern. The red line is a strong link, the dotted red line is a weak link.

Where the 1 goes, is in one of two patterns below.

Pattern A

Pattern B

When the two patterns are combined, it becomes like the diagram below.

And in the overlapping areas marked X, a 1 can’t be entered. (The X’s of the strong link are not shown.)

## X-Cycles 4

Below is an easy pattern.

As you can see, 1 can’t be in the areas marked with X’s.
Examining the samples, in each case, the connection in the weak link, if it is a row or column, that row/column’s other cells are removed as candidates. If it is a box, the box’s other cells are removed as candidates.

If you can use this technique, you are quite accomplished at Sudoku.

## Names of cells in Sudoku

 A1 A2 A3 A4 A5 A6 A7 A8 A9 B1 B2 B3 B4 B5 B6 B7 B8 B9 C1 C2 C3 C4 C5 C6 C7 C8 C9 D1 D2 D3 D4 D5 D6 D7 D8 D9 E1 E2 E3 E4 E5 E6 E7 E8 E9 F1 F2 F3 F4 F5 F6 F7 F8 F9 G1 G2 G3 G4 G5 G6 G7 G8 G9 H1 H2 H3 H4 H5 H6 H7 H8 H9 I1 I2 I3 I4 I5 I6 I7 I8 I9