Hajime wrote:yzfwsf wrote:(5 = 7) r3c2 and (7 = 6) r6c1 are not in the same house, and the candidates(5 start/6 end) are not the same, so you cannot form any eliminations.

Can XYchain not be reversed? So head/tail swapped? Than (7start/7 end)

No no, not so bright Hajime ! The 5 and 6 needs still to be compared in a reverse XYchain. So no valid XYchain.

Thank you yzfwsf. I am convinced that all XYchains can be reversed.

So to find an XYchain for a certain cell you only have to search for two pincer cells (head/tail) where the head-cell is earlier (in reading order) than the tail cell.

Next question:

I like the two-coloring of candidates of the images. So if we search for a 5 in the head (cell 1) and tail (cell n), that must be of different colors (say orange/green) to have a valid XYchain. Let 5 in head-cell be orange. Than a green link will be there from cell 1 to cell 2, an orange link between cell 2 and cell 3, etc. We need to end with an orange link between cell n-1 and cell n. Conclusion: the length of an XYchain has always an odd number. Right?

Do your solvers stop searching after the first found XYchain or do you proceed to find a possible shorter chain?

Is there an XYchain in the above puzzle of length 5? You only have to find one elimination in this puzzle to have stte.