## Arnold Abandons Reason

This post calls out Arnold Snyder’s embrace of arbitrary guessing as a way around the inadequate advanced Snyder methods in Sudoku Formula 3. I also deplore his misguided endorsement of Peter Gordon’s Sudoku Guide.

If the puzzle survives the “Snyder Method”, Arnold advises that you “forget all the difficult stuff”. If it has plenty of bi-value cells, use Arnold’s ultimate weapon, the grandly titled Impossible Force. Arnold doesn’t say what to do, if it has only a few bv. Maybe that’s what Sudoku Formula 4 is all about. I’m not going to find out.

So what is the Impossible Force? Following in the footsteps of his mentor, Peter Gordon, Arnold doesn’t tell you what anything is, but only in great detail what you do to verify that his example works. Or in this case, he does describe the process, because it’s not difficult. Here is his overall description of how you “find” the impossible force: “You find it by taking any cell that has only two possible candidates. Assume that one of the candidates is the actual number, then follow the trail to see where it leads.” That means solving until you reach a contradiction or a solution? No, as you read on in Sudoku Formula 3, you discover that “where it leads” means solving until you reach a contradiction, a solution, or a “dead end”. Arnold doesn’t believe in learning “the difficult stuff”, so he reaches many dead ends. That’s why he goes for the impossible force only when he has many bv cells to try.

That excuse for arbitrary guessing is embarrassing enough, but Arnold also argues that the impossible force is actually a logic based method. He gives us several examples where the choice of the wrong bv partner leads to a conveniently quick contradiction. One of them is the preview puzzle #19, with the Sysudoku basic trace:

Arnold’s order of battle yields a swordfish which is quite evident on the Sysudoku 8-panel. His next comment, though, is telling. He notes the lack of more fish, slipknots, or classic cycles, then asks,

“Do we have to start looking for the really weird patterns like jellyfish or squirmbags? Do we need to find some erratic cycle pattern that’s not rectangular? Do we need to look for a different type of pattern that we’ve seen discussed online but that’s not even mentioned in this book, like an X-Y-wing, or and X-Y-Z-wing?” (Arnold’s names.)

Arnold avoids this “difficult stuff” by “assuming” that 4r4c1 is the “actual number”, and following the trail to see where it leads. Conveniently it leads to a contradiction in a nice rectangular pattern, ending as 3r9c4 implies 6r9c1 in an “impossible force”.  Arnold then announces that the collapse from 4r4c1 can be verified by the answer in the back of Sudoku Formula 3.  Case closed, and Arnold moves on to more examples, even using Peter Gordon’s Repetitive Bilocation Cycle as a “too difficult” strawman he can bypass by arbitrary guessing. I won’t waste your time with that, but of what “difficult stuff” in Formula 3 #19 does Arnold’s “impossible force” leave him unaware?

Well, the XY-chain railroad, would have shown him a large number of his “classic cycles”, and he might have realized why they are often ineffective in a cloud of related bv.

Since Arnold does “classic cycles”, he could do certainly find XY-chain ANL, if only he undersood alternative chain logic. He would know all about “hard stuff” XY-wings as a bonus.

And by being no more systematic than he is in pursuit of his “impossible force”, Arnold could find many ANL (almost nice loop) eliminations. Here are three of them, with toxic ends marked. Extensions to the inner chain remove 6 and 8-candidates, but the removal of the inner chain, the 4-candidate, removes the other two and finishes the puzzle.

And of course, with such an extensive network of bv, why not color? Here, Snyder has allowed himself to be mislead by the one writer he endorses, Peter Gordon. Gordon has him believing that Medusa coloring is a way of seeing where his guess leads.

He has totally missed an easy way to exploit the puzzle’s network of strong links, made extensive by the bv. That network is a fact on the ground, like the bv themselves. It is there regardless of which candidate Arnold guesses is true.

In this case, the easily applied cluster covers the bv field. It traps two candidates for one clue, and forces two green candidates in r8c1, and two green 6-candidates in r8, a color wrap that declares all blue candidates true. So easy. So decisive. Such a testament to the willful Sudoku ignorance of “experts” Arnold Snyder and Peter Gordon.  Instead, Arnold finishes his puzzle with another “Impossible Force”

On a brighter note, I can report that Arnold’s #19 also produced the only example I have so far of an irregular XY-wing, and this with an interesting kicker. The wing, in red, is an XY-chain of length 3, with toxic end 6-candidates. The 6r6c6 victim sees one of them directly, and the other, by ER, illustrated by a grouped forcing chain. This is the kind of fun in store for Arnold when he invests more deeply in Sudoku.

Then look at what the iXY-wing removal leaves behind, a BUG +1 resolved by Stuart’s three candidates per unit rule.

Next, we defend the honor and living space of a seldom seen but still remembered friend, the WXYZ-wing. We hope to give two rivals their own apartments, so they can move out and leave our friend some breathing room.  After that it’s on to a Hodoku review. Now get out there. Summer’s waning.