Fishy Cycle

A Fishy Cycle is a continuous loop of candidates for a single digit. It has alternating strong links and weak links.

The Fishy Cycle was first introduced as a generalization of fish patterns like X-Wing, Swordfish and Jellyfish, before these patterns were seen as constraint sets. At that time, players believed that each defining line should contain only 2 candidates. There are still some websites that contain this old definition of Swordfish and Jellyfish.

An example may help you understand the concept:

 ------- ------- -------
| - X - | X - - | - - - |
| . : . | : . . | . . . |
| - : - | X - - | X - - |
 ------- ------- -------
| - X - | - X - | : - - |
| . . . | . : . | : . . |
| . . . | . : . | : . . |
 ------- ------- -------
| - - - | - X - | X - - |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
 ------- ------- -------

Rows 1, 3, 4 & 7 all have 2 candidates. A cycle can be formed by connecting these candidates using the columns. The resulting cycle is:

r1c2 = r1c4 - r3c4 = r3c7 - r7c7 = r7c5 - r4c5 = r4c2 - c1c2

This pattern is a Jellyfish. We can eliminate all remaining candidates for this digit from columns 2, 4, 5 & 7.

A Fishy Cycle does not need to be restricted to rows and columns. Boxes can also provide strong or weak links. Here is another example:

 ------- ------- -------
| . . . | . . . | . . . |
| - X - | - X - | - - - |
| . : . | . : . | . . . |
 ------- ------- -------
| . : . | - - - | . . . |
| . : . | - X - | . . . |
| . : . | - - X | . . . |
 ------- ------- -------
| . : . | . . : | . . . |
| - X - | - - X | - - - |
| . . . | . . . | . . . |
 ------- ------- -------

This cycle uses 1 box and reads:

r2c2 = r2c5 - r5c5 = r6c6 - r8c6 = r8c2 - r2c2

Remaining candidates can now be eliminated from columns 2, 5 & 6.