## Hanson’s Strong and Weak Hinges

Continuing our intense review of Bob Hanson’s web report on Sudoku Assistant, I found no useful additions to the Sysudoku repertoire in the next few sections, so they just get a mention in passing. Then we examine Bob’s simple but worthwhile human solving idea, strong and weak hinges. Also I unload on Bob’s Medusa variations.

If you’re following along in the report itself, I’m skipping the result tables on SA solving options at the end of Almost-Locked Ranges and the options on the level of ALS analysis in The Sudoku Assistant and Almost-Locked Sets. I’m not planning to run Sudoku Assistant myself.

This brings use to a truly befuddling section entitled 3D Medusa Analysis. After what looks like a reference to a network of forcing chains, we get to:

“What is significant is that in a “binary grid” every other cell along the grid either has one value or another — only two possible values. (The grid is made by specifically selecting only cells that have exactly two possibilities.) If any two such cells are in a single row, column, or 3×3 block, it is as if they were the ONLY possibilities for their cells.”

Is Bob talking about the bv map, or an alternating inference chain, or an XY-chain of bv cells? Are the “values” numbers, or TRUE and FALSE?   And is the last sentence describing a naked pair? This was covered earlier in the SA report.

A translation of the example diagram that follows is:

From this, Bob must be talking about a strong link network with one candidate seeing both polarities. To my readers, it’s a coloring cluster and a simple trap.

OK, after admiring a 3-D picture depicting all slinks on all numbers, including bv cells in the vertical direction, let’s move on.

I thought I would finally see how Bob would explain alternative inference chains when I began his section, Weakly Linked Chains, but it was not to be. He is talking about AIC, but his treatment of winks and slinks is both restrictive and vague. He goes on about the “strongness” or “weakness” of chains and nodes, without explaining what he means. I gave up trying to make sense of it.

In the next section, 3-D Medusa Hinge I did find a humanly useful idea. It is based on this rather obvious observation: If two outside candidates combine to see all candidates of a number in a unit, then they cannot both be true. Profound, isn’t it?

Bob shows us what can be done with this idea. In his “strong hinge” example, the hinge unit is a box. The North box insists on

not(Xa and Xc)

but the forcing chains between them say that

Xa => Xc and Xc => Xa.

The only way out is not Xa and not Xb.

In Bob’s diagram, the forcing chain nodes are bv cells XA, XB, AND XC, suggesting that the technique requires bv cells. It doesn’t. Any forcing chain will negate its originating candidate. Like Paul Stevens, Bob is having cells linking, instead of candidates linking. It limits and obscures the technique.

Bob calls this idea a Weak Hinge when applied to a line. Once we agree that r2 contains no more candidates X, the row insists on

not(Xa and Xc).

Because of the wink, we can proceed only from Xc, but it follows that

Xc => Xa .

This time Xc is removed, but the news does not reach Xa or Xb.

It’s something to watch for, but just one more thing. The title of this section, 3D Medusa Hinge, suggests that a Hanson theme, the use of number values in a cell as a third dimension, applies to the hinge idea as well. In fact, Hanson says:

“Medusa variants also target cells in the same row or column, or target values in the same cell.”

To follow up on that, go back to the profound observation above, and imagine what the two outside candidates are, in these variations. Instead of fixing X on a single value, pick a row position. Then columns and number values are the other two dimensions. A box is the numbers in a range of 3 in the same column. OK, what is a crossing line? Now what is an outside candidate? Mind boggling, isn’t it?

Now consider this. The translation of the row/column version of a puzzle to row/number or to column/number versions is a simple computer algorithm, as is the translation back. All computer solving algorithms are good in that other space.

To me, Medusa variations of human solving techniques are interesting, but useless. But to a computer solving enthusiast, its hard core. I’ve been quite hard on Bob, but remember, he’s a leader in the computer solving camp. It’s not the same game.

Next time, I conclude the review of Bob’s Sudoku Assistant report. We’ll all be relieved. But fair warning, I’ll be on my T&E soap box.