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2021-10-24T18:32:03Z

Created page with "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 i..."

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A '''Fishy Cycle''' is a [[continuous]] [[loop]] of [[candidate]]s for a single [[digit]]. It has alternating [[strong link]]s and [[weak link]]s.

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 - r1c2
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.

[[Category:Solving Techniques]]
[[Category:Chains and Loops]]

Fishy Cycle - Revision history

127.0.0.1: Created page with "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 i..."