Suppose an X-chain of length 8 and the cell-numbers are 1-2-3-4-5-6-7-8, and the target candidate is '3'.

Odd-numbered cell have '3' OFF, even numbered cells have '3' ON.

Strong link between odd-even and weak link between even-odd cells.

Rule: all cells that 'see' cell 1 AND 8 can eliminate '3'. Start-cell number is 1 and end-cell must be even.

Now an optimization:

A. all cells that 'see' any odd-numbered cell and any even-numbered cell can eliminate '3'.

Further: The X-chain will be extended with cell-number 9 and it collides with the chain itself.

If it collides with an odd numbered cell, say 5, (cell 5 and 9 are the same) we get an continuous nice loop (X-cycle).

B1. All cells that see both an even AND an odd numbered cell between 5 and 9 (same cell) can eliminate '3'.

B2. We cannot say anything about cell number 1.

B3. If statement A is correct, statement B1 is already dealt with.

If it collides with an even numbered cell, say 4, (cell 4 was ON and must be OFF ) we get an discontinuous nice loop (X-cycle).

C1. Cell numbered 4 cannot have '3'.

C2. Cell number 1, that lead to cell 4 has a '3', is also false and must be '3'.

If the X-chain was of odd-length (say 7) and extended with cell 8 then

If it collided with cell 5 (odd number) :

D1. Cell 5 must be '3', other candidates in cell 5 to be eliminated.

D2. Cell number 1, that lead to cell 5 not having a '3', is also false and must be '3'.

If it collided with cell 4 (even number) :

We get a continuous nice loop

E1. All cells that see both an even AND an odd numbered cell between 4 and 9 (same cell) can eliminate '3'.

E2. We cannot say anything about cell number 1.

E3. If statement A is correct, statement E1 is already dealt with.

B=E and C=D depending on odd/even.

Are all statements above correct? Did I miss something?