Gould’s Not So Fiendish

This post begins a review of Wayne Gould’s Fiendish collection in his Train Your Brain Su Doku. The review is an opportunity to take up an important issue in basic solving, the use of pencil marks. For the ten preselected puzzles of the Fiendish review, instead of the dublex bypass of recent posts, I begin box marking without pencil marks. I checkpoint it in a separate trace, labeled “No pencil marks”, or NPM. This Wayne Gould review concludes my series of posts on basic level collections, and my clinic on basic solving.

fiendish 85 npm trHalloween is over, but was Fiendish 85 a trick or a treat? I was surprised that NPM carried me to a solution. Here is my 2-D trace.

Read it by filling the grid as you go and supplying your own reason for each effect, given the cause and the state of the puzzle at that point. Except that with NPM you have to remember candidates of that state.

Actually, my trace follows the same path as the usual slink marking. Without pencil marks, however, you have to remain aware of the slinks and naked subsets you are not allowed to write in. A good example is 6: S3. This necessary “marks memory” is also responsible for N7.

Any remaining mysteries should be resolved by following the regular slink marking 2-D trace. I carry it below to a point where it is no longer necessary to keep marks and closed sets in mind,

fiendish 85 bm tr

fiendish 85 slinks gridwith the grid now looking like this:

I know several Sudoku solvers who operate without pencil marks, but I haven’t investigated how they do it. The Fiendish 85 example illustrates how a sysudokie, accustomed to slink marking and closed subset marking, could do it on a basic level puzzle.



For the review, I preselected every 15th puzzle starting with Fiendish 10. The table includes the number clues I was able to add in the NPM phase, with a reasonable effort. Let’s consider it an average sysudokie performance, with many of my readers doing better.

fiendish review table

For two puzzles, the collapse (—-) was reached in the NPM phase of box marking. With one exception, there were very few clues added in box marking after NPM, suggesting that the NPM clues are those normally found in box marking anyway. The exception is definitely an outlier, being a multiple solution puzzle.

Another very noticeable feature of the collection is that it is definitely basic level. Line marking is generally easy, when it is necessary. Fiendish? Hardly.

Wayne Gould is a very successful purveyor of a computer solver, and a long standing supplier of daily puzzles to newspapers. Peter Gordon, again in his Mensa Guide to Solving Sudoku, relates how Wayne became well known in Sudoku history. It wasn’t his knowledge of human solving, or his opinions of pencil marking, as quoted in Train Your Brain Su Doku Fiendish. Wayne says:

“If you are writing too many pencil marks, it means you are not understanding how the puzzle works. You may be relying too much on mechanical procedures, without appreciating the underlying logic.“

At first I was aghast at this proclamation, until I realized that nowhere did Wayne specify what “too many” means. Maybe he wasn’t dissing slink and subset marking at all. He could have been making a valid criticism of the inefficient, mechanical process of finding candidates by number scanning that we have called out expert after expert for advocating. Number scanning is indeed a mindless operation that does indeed generate too many candidates, and too many pencil marks.

But then Wayne goes further, with “If, in time, you can shake yourself free of written pencil marks, you will see the Su Doku puzzle for what it is – a thing of beauty!” By the special spelling we are to understand that Wayne means his puzzles

Now that’s going way too far! Here Wayne must mean all pencil marks. And only if you go without them, can you behold the beauty of his puzzles. That’s ridiculous. I agree that keeping the marks in mind, and not on paper, is good mental exercise, but it’s going to expose less logical truth, not more. Take my own results in this post, for example. In the review, my NPM home runs were 2 of 10, but my basic collapses by slink marking were 10 of 10.

And what about advanced methods? Are you prepared to remember all viable candidates so you can do the advanced repertoire blindfolded?

Wayne’s opinions on underlying Sudoku logic will get more respect when he demonstrates  genuinely advanced and extreme level Sudoku solving.

What’s your opinion on solving without pencil marks? And do you think those who do it, on very tough puzzles, are really solving? Or could they be doing simple trial and error? That can be a mental challenge, but it is not solving by the Sysudoku definition.

As to the Fiendish collection, I have several tasks in mind to do, all bearing on the pencil marking issue.

fiendish 130First, I’ll checkpoint Fiendish 130  the same as I did 85, giving readers another shot at one for which a legitimate NPM collapse is within reach.  That will be next post .

Then I’ll examine one with which I had the least NPM success, Fiendish 145. I intend to use the successful regular slink marking to show what mental gymnastics would be necessary for NPM there.

Next, I’ll demonstrate a puzzle for which the difference between NPM and the dublex bypass is stark, Fiendish 41. It’s not a review puzzle, but one I encountered in the car service department waiting room.

Finally, you may be interested in the analysis discovering the 12 solutions of Fiendish 100.

If you have Train Your Brain Fiendish, you can go on ahead and start uncovering all of these fiendish secrets. Meet me at the passes.


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.
This entry was posted in Basic Solving Procedures, Expert Reviews, Puzzle Reviews and tagged , , , , , . Bookmark the permalink.

1 Response to Gould’s Not So Fiendish

  1. Pingback: Adopting the Slink Marking Bypass | Systematic Sudoku

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