## Bob Hanson’s Sudoku Assistant

This post introduces my review of Bob Hanson’s web report on his remarkably constructed Sudoku Assistant solver. The report is on his St. Olaf University website page, and is titled Sudoku Assistant – Solving Techniques. This comparative analysis is not undertaken to  criticize the Sudoku Assistant, but to uncover new human engineered solving methods for sysudokies.

Yes, Bob Hanson is the co-author of the HM Easter Monster paper we just spent some profitable time with. Bob is a chemistry professor by trade, a mathematician by inclination, and is known in the Sudoku community as an expert computer solver programmer.

Based on Bob’s introduction, we can align the Order of Battle of the Sudoku Assistant (SA) with the Sysudoku SSOB this way:

An SA basic phase, leading to candidates not excluded by locked subsets, consists of a number scan for candidates, cross-hatch scanning, row/column range checking, and subset elimination. I will compare these methods to Sysudoku box marking and line marking.

An SA advanced phase, consisting of grid analysis, bent naked subsets, almost-locked sets, 3-D Medusa analysis, finned fish and sashimi, and almost locked ranges. I’ll compare these with the Sysudoku advanced methods with regard to ease of recognition and completeness.

An SA trials phase, which Bob calls hypotheses and proof, and which may provide insights on the issue of necessary and efficient trials vs. simple trial and error.

It is easy for us to read into Bob’s SA report as being about human solving. We see statements like “Once all the singles have been found, I usually start marking.” But this report is not at all about solving by hand. Sudoku Assistant is a solver, and not so much an assistant as an elegant demonstration of the power of Hanson’s unifying generalized method:

Bob wouldn’t be so flippant, but I can’t resist. I’m going to refer to the generalized method as GM.

Sudoku Assistant is a remarkable engineering accomplishment, but not a human engineering one. Our first task is to understand the GM rule itself. Bob describes A and B of this rule as “some number of rows, columns, cells, or blocks(to us, boxes)”. But it’s not enough to take A and B simply as sets of cells or candidates, as represented by the standard Venn diagram.

This is a Sudoku theorem, not a set theorem. Bob knows what he is talking about, but he forgot to tell us. A and B are sets of cells, lines or boxes which are known to contain exactly one true candidate (or set of true candidates) of a number k. This feature is essential to the GM rule. If there is no true candidate (or set of candidates) k in A elsewhere, it must be in the intersection, and if B has more than one true k candidate(or set of candidates), it can have one outside of the intersection.

The cell sets A and B containing exactly one true candidate of a number are the “truths” in set link theory and our toxic sets. Bob has many more uses for them, however.

Finally, we need to fully understand what “ is possible” means. In applying the GM to a particular type of A and B, “is possible” means that the intersection must contain one true k, by the properties of Sudoku. And “is not possible” means that k candidates are not among the known candidates in the A cells, and therefore cannot be in the remainder of B outside of the intersection.

Our comparisons must take into account that SA “knows” the rules of Sudoku only as a set of operations on the solving state of the puzzle. In evaluation for human solving, we must take account how humans can and must bypass thousands to millions of operations by direct observations.

As background for the next post, on Assistant basic solving, I suggest doing our version on Bob’s first example. If you’re a sysudokie in good standing, do a 2-D trace, at least of the box marking. Take your time.  This assignment is due in two weeks.