I start my review of Sudoku Assistant – Solving Techniques with the basic solving of Hanson’s Sudoku Assistant, introduced by last week’s post. Basic solving is defined as the process by which we complete the candidate grid, required for advanced solving.

The generalized method of the previous post is Sudoku Assistant’s showcase rule, but Bob advises we should start with hidden singles, which are defined by his general rule of singles:

The rule would be more aptly named the “rule of hidden singles”. I hope Bob will forgive the parenthesized paraphrases. Where necessary, Hanson’s terminology and notations will be translated into Sysudoku speak, so that my habitual readers, the sysudokies, will have less difficulty understanding what he is saying.

Bob introduces this rule as a basis for the robot’s first step, cross-hatching, a scan of boxes for hidden singles. He notes that “hidden singles are far easier to find than naked singles”. I second that motion, having rejected Tom Sheldon’s beginning search for naked singles, his completion strategy, in favor of having them emerge in line marking. I therefore associated hidden singles only with lines. I guess I got pretty far without noticing that box marking clues are hidden singles.

Bob’s cross-hatching combines my cross-hatching with the double line exclusion in “clue only” box marking. This is also the Paul Stevens approach. Bob comments that this scan sufficient for easy puzzles, and that many do it without marks. In the Stevens review, we found it lacking in puzzles that talented solvers do solve without marks, noting the “marks in the head” these solvers are carrying. But actually, I believe we should ignore any such comment in Bob’s report about what people do, for reasons I’ll get to shortly.

In Bob’s illustration of the cross-hatch, there is nothing wrong with your computer screen. The dots belong in r3c5. It is a way to represent candidates by dots in their keypad positions, and is handy when the grid is packed with candidates. Here Bob is just pointing out the four candidates 4, 5, 6, and 8 that would have occupied r3c5 if the Nhs5 had not been discovered.

The Sysudoku position is that finding box strong links is just as easy as hidden box singles, and should be done at the same time, adding remote pairs and naked locked sets to the Paul Stevens’ claimants for available box cells, thereby generating more clues and fewer candidates. In the Paul Stevens review, I acknowledged that this more comprehensive box marking could be done box by box, as well as the Sysudoku choice of number by number, but I stick with 1 through 9 throughout Sysudoku to maintain a consistent trace.

Bob is saying that all hidden singles are found in the Assistant’s first step. This would include line singles that turn up frequently in line marking, but he says nothing about how they are found. If you are a newbie, Sysudoku line marking is a line by line analysis yielding all candidates, line slinks, bv cells, box and line closed sets, and immediately available X-wings. So I’m looking for some corresponding process on the way to the candidate grid. How and when does Hanson get to the low hanging fruit of boxed remote pairs, aligned triples and naked pairs in basic solving?

Next, Bob presents the first two special cases of the generalized method rule. He classifies them as row/column range checking, and names them the locked candidate rules, form 1 and 2. In both rules, A is a chute, the intersection of a line and a box. Form 1 says that the absence of a candidate k in the line remainder (elsewhere in A) removes all candidates in the box remainder (elsewhere in B). Form 2 says that the absence of a candidate in the box remainder (elsewhere in A) removes all candidates in the line remainder (elsewhere in B).

Assuming you are still awake, do you recognize these rules? Of course. Form 2 is about the remote pair and aligned triple removals in box marking and later. Form 1 is a boxline removal.

Bob’s illustration of the Form 2 (N1m marks) in action answers my question above, and a lot more. Bob draws arrows showing the remote pair r3c23 removing two candidates, leaving two in the NE box. But he draws them on a Sheldon “completed “ grid, which I have reproduced here on a Sysudoku template. Bob’s “marking” is Sheldon’s “completion” strategy.  I long ago rejected it as a human solving tactic, calling it the “number scan”.

In  reviews I normally transcribe a keypad candidate grid into a Sysudoku one, for my readers. But this one has too many unslinked candidates. That’s why keypad candidate grids from elsewhere have such tiny fonts for pencil marks, or have candidates represented by dots. Of course these remedies do nothing to reduce the visual complexity of a sea of candidates.

I did the “completion” of candidates from the original clues myself, then checked my work against Hanson’s. I had made a few mistakes. That is understandable because the process is booooring. Nothing worth thinking about is going on. I made a list of marks 1 through 9 down the right side of the grid. For each row I selected a candidate number (not a clue) in the row and dragged a copy of it into its keypad position in each row cell without that number it its column. Its 10 times more mechanical than line marking.

We don’t really care how Bob does the completion by hand, or how  Sudoku Assistant does it. The fact is, every computer solver has to do the completion of candidates first because the “completed” array, now represented by the keypad numbering in the diagram above, is the way a computer sees or draws the arrows. Think about it.

You can reproduce the computer algorithm yourself, but it is even more boring than my method above. To play computer, make up a 9 by 9 array of lists 1 through 9. That’s 81 lists, you know. Then for every given clue, delete the clue number from the lists of all cells in its row, column and box. You can see how Sudoku Assistant actually does range checking by following the ‘x’s above. The red arrows were “drawn” in the completion scan. In the range checking scan, SA observes that the only 1’s are in NWr3, and consequently, it removes 1’s from cell lists along r3. Were you confusing the 1’s and x’s on the top row with box marks? No, there are no box marks. Box marks are signposts for humans, denoting strong links and why they are strong.

You can see why Sudoku writers, most of whom are programmers, offer nothing better than the completion algorithm in their solving advice. Because of this, the elegance and fun of basic solving that many of my readers have discovered in the elaborate basic solving traces of some puzzles, is compromised or completely obscured by the completion algorithm. Even experts are deprived. And those who are uninformed and naturally gravitate to the completion algorithm get a discouraging false impression of Sudoku solving by brain.

So now we understand how line hidden singles are found. As SA deletes clue numbers from cell lists, it can easily track how many cells are left for each number in each line. When that number gets down to one, SA has a hidden line single. Voila! Just one more thing. SA can do the same for boxes, so why do we need cross-hatching? The answer is, SA doesn’t, but we do. I think Bob’s cross-hatching is a human interpretation of what an inhuman algorithm actually does.

In Bob’s report, he leaves one hidden box single “missed” in the cross-hatching for readers to find. You can find it as SA does, by tracking the candidate lists above. But you’ve already found it, so circle it on your trace.

Next, mark Bob’s first range checking example on your trace, the NWm =>NEm. It’s an ordinary elimination with an aligned slink.

The second “marks elimination” example on the candidate grid above is W9m => C9m. Play computer and carry it out on the candidate lists. What happens to that one in your box marking trace?

Next week I’m taking time out to checkpoint your basic solving of Bob’s illustration puzzle. This post got a bit long for that. Then we will closely scrutinize the next basic subject of his Sudoku Assistant report, locked sets. If you didn’t do that homework already, it’s not too late. There are some nice examples of locked sets waiting to be discovered.