## The Fiendish 100 BUG-gy Maze

Bad news for Su Doku Master Wayne Gould. Fiendish 100, the only “Fiendish” of our Train Your Brain Su Doku Fiendish review to survive line marking, is found to have at least 15 solutions. The solutions are revealed in multiple BUGS, an irony in itself, since a BUG can be expressed only with the pencil marks that Wayne urges us to do without.

To begin the Fiendish 100 report, here are the dublex bypass and box marking traces, followed by the resulting grid.

Line marking depends on two naked singles, and deals with many triples.

Would you want to do it without pencil marks?

I didn’t think so.

There is not much for advanced techniques to do, but to start, I find a potential  Sue de Coq in

Nr2=6(1+5)(2+7)

+627 +672.

To eliminate 5r2c2, I have to verify it, by proving that 15 is not missing, leaving Nr2 = 627 +672.

The trial trace runs right into a Bi-value Universal Grave. I color the two solutions immediately.

Despite the name, a BUG is not a death sentence for the composer, but it is a big black mark. It’s not supposed to happen. Some “experts” recommend solver eliminations that prevent an iminent BUG on the theory that the composer could not possibly have foisted a multiple solution puzzle on the public.

I have found that, instead, composers sometimes do that. We should expose composers who do not fully employ readily available computer technology to prevent multiple solutions. Note that I am not talking about unique rectangle eliminations, but complex BUGs such as this one.

When a multiple solution is encountered, it signals a slippery region of puzzle logic that accommodates multiple inputs and gives the solver no logical toe holds to climb on. In this case, the faulty Sue de Coq verification BUG left me with the suspicion that more solutions may be lurking in beyond the failed Sue de Coq’s 5r2c2 elimination. It turned out to be at least 15 solutions.

I decided not to post the seven additional grids necessary to show how the solutions are derived, but those interested can ask at sysudoku@gmail.com  for the PowerPoint solution file for Fiendish 100.  The search follows a pattern I’ve used before. Use the Find It page above to find them.

The NPM challenge was fun, but it won’t be continued in the Order of Battle. I believe this collection was tailored for NPM, in tune with Wayne’s beliefs. We have adjusted Sysudoku basic solving toward NPM, by including a dublex bypass in box marking. I believe the combination is a little more efficient than box marking alone, on average, and adds a challenge .

The Fiendish puzzles are a treat for basic solvers, NPM or not. On a road trip, my grandson Daniel and I had a solving contest with them. He won.

Before I begin the review of Peter Gordan’s advanced solving instruction, ending the basic clinic, I’ll be posting my annual report on the Akron Sudoku Tournament, put on by the Akron-Summit Public Library, with the support of Will Shortz. The puzzles are basic level. You will learn how my dublex bypass for timed contests would have fared in the hands of the rapidly thinking winners, as opposed to me, in whose hands it failed decisively.

Participants who have the puzzles will be able to get sysudokie traces for all the puzzles by request on sysudoku@gmail.com. In the post, I’ll have a review table including all tournament puzzles, and a full trace of the championship puzzle shown here.