Closing Very Hard v.2 with the Real 38

To be fair, here is my do over of the real Ardv2 38, the one with a given 7 in r7c6.  My omission of it hatched a productive distraction, having no bearing on the collection it came from.

The basic solving is not much different, and closes with the same 9-wing. But this time, there is a naked pair nestled on the 9-wing, and a naked single in the South box.

As before, the first advanced step is the Type 4 Unique Rectangle. This time it closes r1.

And this time, the AIC slinks are unnecessary. The 9’s coloring is supplemented by an XY nice loop.  One nice about it is, candidates seeing both ends of any link of the loop are false.

The coloring already claims one trap, and the nice loop brings two more, 7r2c9 and 4r7c4.

But there’s more to the nice loop. Every other candidate on a nice loop is true. If a coloring cluster overlaps a nice loop, it tells which loop candidates are true, extending the cluster.







As the cluster grows, more bv are added to the XY arsenal.  This XY-chain resolves a naked pair for another extension.

At this point, green is caught forcing two 1’s into c9. Green is removed and blue readily confirms Ardson’s solution.

In conclusion, the 38 reliance on the Type 3 UR, the 9-wing and nice loop coloring helps to assure that the Very Hard v.2 collection is broadly advanced in difficulty level.  As to being “Very Hard”, that depends more on your own level of understanding, which is bound to grow with mine as we continue to explore human Sudoku solving.

Here is the review table for Ardson’s Very Hard Sudoku v.2:

Now with the review completed, next post will redo the troublesome miscopy of 38. It is a reminder of the profit that attends keeping an open mind about our mistakes.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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