ravel wrote:Before i look for more complicated chains, i try to combine strong links and should spot the eliminations from bidirectional x-cycles, which are built of strong links only.

I dont look for bidirectional y-cycles explicitely, but sometimes stumble on one, when i look for (extended) xy-chains and come back to the starting number.

Hi, ravel,

At least one person, looking for cycles like me. I made even a puzzle-collection with sudokus who requires cycles only in addition to pairs, UR's, Swordfisches, X-Wings, XY-Wings etc. avoiding any forcing chains, because they can be laid so arbitrarily throughout the whole sudoku, while cycles are well defined like Swordfishes.

Well, a forcing chain everybody may spot somewhere but to find such a bi-directional cycle is a high and beautiful art in sudoku-solving which doesn't unveil itself to everyone.

You wrote you look for bidirectional X-cycles, which are built of strong links only. Unfortunately until now I produced only few sudokus who expose such cycles and even less examples with such bi-directional x-cycles excluding additional forcing chains.

Most cycles are the simple bi-directional, which for me are the most difficult to spot, especially when they include more then 4 cells. Y-Cycles on the other hand I can detect more easily, but I still miss some eliminations when they produce many. But until now the eliminations I found were enough to solve the puzzle.

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`. . 4 . . . 5 . 2`

. 7 . 2 . 1 . . .

. . . . 9 . . . .

7 . 6 . . . . . .

. 3 . . . . 1 7 .

2 . . 1 . . . . 9

4 9 . . . 2 . 6 .

. . . 9 4 . . . 3

. . . . . 7 8 . .

This one is a sudoku which requires no forcing chains but includes a bi-directional y-cycle as well as a bi-directional x-cycle in addition to other fancy techniques.

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` `

. . 4 . . . 6 9 .

. 8 . . . 6 . . 1

. 1 . . 7 . . . .

. 3 . . 8 9 . . .

. . 1 . 4 . 2 . .

. . . 3 6 . . 4 .

. . . . 2 . . 8 .

9 . . 5 . . . 7 .

. 7 6 . . . . . .

I borrowed it from my thread. It requires a Turbot fish and a bi-directional x-cycle only.

regards

Claudia