In the "Exercise on xyz-wing and xy-chain" topic Scott H draws attention to David Eppstein’s paper “ Nonrepetitive Paths and Cycles in Graphs with Application to Sudoku “. In Figure 11 the author shows "one of the more difficult" puzzles. Nothing daunted, I thought I’d give it a go and succeded only in reaching the following point

56x|xx1|xx8

xxx|5XX|6xx

xxx|x62|57x

--------------

x9x|2x5|18x

xx4|x1x!3xx

xx8|3x9|x2x

--------------

x76|98x|xxx

xx5|x2x|8xx

8xx|15x|xx3

after which there is quite a lot of tidying up possible through couples, locked rows and columns such that the cell with the highest number of candidates is r2c1 with 1, 2, 4, 7 and 9. But finally I reached an impasse. I’ve filtered for x-wings, swordfishes and xy chains, searched for hidden triples and quads but nothing.

According to the paper it is solvable using the techniques given there (but in very mathematical terms so not for ornery mortals). However it does imply that trial and error is not one of their techniques.

So is there anyone out there who can see how to solve this puzzle? Presumably Eppstein's so-called repetitive and non-repetitve cyles might play a part but their operation seems horrendous - are they part of the serious player's toolbag?