Perhaps someone can help sort out the logic of this puzzle. There is a NiceLoop which allows the 6 to be removed from r2c3 and from r8c3 and the 2 and the 6 from r2c8. At this point there is an xy-chain that allows the 7 in r2c8 to be eliminated. Proceeding from this point, the puzzle is then solved (and checks with the solution provided on www.sudokusite.eu/pdf/5s-k10.pdf).

But this is where my own puzzlement begins because if you study the xy-chain closely you reach an apparent internal conflict.

Going thorugh the xy-chain in the normal fashion, assume r2c8=7. Then

(r2c3=2) => (r8c3=9) => (r7c3=6) => (r7c8=4) and you can continue to show (r1c8=7) hence establishing the contradiction.

But if you go back to the statement (r7c8=4) then this also carries consequences:

(r7c8<>6) => (r6c8=6) => (r6c8<>2) => (r1c8=2); or more directly (r7c8=4)=> (r2c8=7) which is not in conflict with the initial premise.

The source of the contradiction is the odd number of links from r7c8 round to r6c8 that reverses the logic. I know that an xy-chain cannot use the target cell which in a sense I am doing if the aim is to get from r2c3 to r1c8 but surely the knock-on consequences of the real chain shouldn’t throw up inconsistencies en route.

Any assistance to get my thought processes back on track gratefully received.