## Hidden Candidates of Hidden Logic

This post calls out the useless reporting scheme in place throughout The Hidden Logic of Sudoku, with a checkpointed hidden triple example that sysudokies have solved as homework. The Akron Tournament final checkpoint is at the end of this report.

Royle 17-13727 is chosen in THLS as “the one with the shortest resolution paths (apart from NS and HS) among those requiring HT.”  Denis is referring to naked and hidden singles and the hidden triple, with “hidden” having its usual meaning, not involving “hidden logic”.

My readers who have not seen a copy of THLS might be thinking the grids and traces in this book are somewhat like those they are seeing in Sysudoku checkpoints, and generating in sysudokie homework. At this time in the review, they might expect to see a hidden triple in nrc space and its counterpart naked triple in a symmetry grid. In fairness, subsets would be shown embedded in the number scanned and transformed sea of candidates that normally inhabit grids in the basic stage of solving.

Readers of THLS know that none of this is available. Unless readers generate it for themselves.

For every example puzzle THLS gives three grids, all in nrc space:  the initial givens, the final solution, and a middle grid, the elaboration, representing the product of rules of logical complexity up to, but not including, the method being illustrated.  The incredible thing, if you haven’t seen it, is that no candidates appear in the elaboration, only clues.

For your Royle 17-13727, Berthier reports the SudoRules L2 elaboration shown here. L2 includes hidden singles and pairs in both senses of hidden, with symmetries and supersymmetries.  We’ll get to it shortly, but just so you know, L2 includes X-wings through THLS supersymmetry. Beneath the three grid,  you are told in text, where the hidden triple is, and what it removes.

You don’t get to see the hidden triple in any context. My question is, without candidates, how does a THLS reader make any evaluation of any example results without doing their own basic solving?   You deserve better. After bypass and box marking, my box marked grid shows two additional resolutions to be made in line marking, namely 8r3c3 and its effect, 2r4c3.

My scan, for fewest free cells and shortest line fill strings, portends a miserable line marking. But I get a break on the second line:

A naked quad 3478 jumps out in NE, leaving only three cells for 5, 6 and 9. This hidden triple exists only when the number scan clutter is added. The box/line removes other 7’s in r1.

The collapse goes on from there, with no need to fill any more lines, and without the 8-clue missing above. It results from a cause held in reserve, at the very end. So I’d really like to know where it came from in the THLS elaboration. Can you help me out there? Yes, I looked for a possible 8-wing from supersymmetry in L2

To resolve my mystery, I number scanned the candidates around Berthier’s elaboration clues. That explained nothing, but it does show the state of the grid, as Berthier reports the post L2 trace to his hidden triple resolution. SudoRules finds the two naked pair eliminations in E, the two hidden pairs, and the hidden triple as a naked triple by symmetry.

The triple would be L3, you know. The naked quad, L4. Does any sysudokie care?

For homework, find these in the sea of candidates here, and imagine the amount of searching it takes to find all of them on a cluttered grid such as this.  I’ll mark them on the grid next time. The next post will also review the THLS treatment of box/line interaction and its relationship to slink marking. Note on your trace or mine how Sysudoku basic finds all of the hidden subsets, without grid transformations and with searching limited to one unit at a time, and with suset backup for diabolical cases. Think about it.

Now for the Akron 2016 checkpoint This is the grid after the slink marking bypass. Translation: Slinks are strong links. In the bypass, you use them, but don’t write them down. The only pencil marks are for conjugate pairs or other subsets.

You can read this trace! Boxes are denoted by compass notation, C being the center box. Lower case r, c are row and column. Naked pairs are “np” and the two digits. The reader supplies the reason. The order is left to right and down each ramp before the next cause. Effects are indented under causes. Lists of effects are read left to right.

Some steps may not be apparent if you’re not used to doing this. These hints might help you catch on to what is going on:   S2m => N2, SE3m & SW3m => SE3, S5m => N5.

Now we continue with the box marking, in which we mark the slinks and aligned triples in the corners and sides of cells. Any time only two candidates of a number remain in a unit, these two are strong link partners. The “m” denotes a box slink (marks).

In Sysudoku, strong and weak links, slinks and winks, are between candidates and not between cells, as many writers suggest. It’s amazing how much confusion this mistaken concept has caused.

Here is the result, ready for the final step of finding all candidates, the line marking. If the puzzle gets this far, it’s worthy  of the stage at the Akron tournament. Much farther, and it’s too difficult for that.

For line marking, find all the cells with only two candidates. Mark them. These are bi-value cells, very important for advanced methods. I call them bv.

Now go down rows and then left to right, looking for  the first line with the fewest free cells. Its row 2(r2) here. If we hadn’t found the naked pair 2,4 in the bypass r1 would start the 3f: list, because the bv 17 cells are not free. They are reserved for 1 and 7.

For r2, I have three free cells to start the 3f: list.  Now you make up a string of numbers that can possibly be added to the free cells. I call it the fill string. My fill string for r2 is 14. I don’t have to include 9, because no 9 candidates can be added. With this much to go on, see how much line marking you can do, and tune in next week’s post for the checkpoint on the fate of the final puzzle. If you want to look at more line marking examples, browse around. Look at the Find It page. Any basic solving posts will do, including the Dave Green Labor Day weekend posts you can scroll back to.

I will also have a bypass trace on that round 3 puzzle.  Build your own trace to match. The experience with the championship puzzle bypass will help. For those not fortunate enough to be in Akron November 5, here is a copy of the Round 3 puzzle.