## What to look for

Advanced methods and approaches for solving Sudoku puzzles

### What to look for

Not sure if this is the right forum for this question. But I apologize in advace if is it incorrect. Also, not sure if the question makes any sense, but I'll give it a try.

Have been lurking here for awhile, trying to increase my sudoku skills. I find that I am reasonably good at learning and applying the techniques that are "pattern-based", like X wing, turbo fish, swordfish, XYwing and also coloring. But, I am very slow to recognize the "chain- based" solutions. So far, the few I have found were after long sessions of trial and error.

I was hoping that some of the more accoplished solvers could provide some hints, tricks or triggers that they use to recognize that "chain" techniques would be applicable to a particular puzzle, and how they select where to try starting and ending the chain.

Thanks in advance for the help.
winelines

Posts: 2
Joined: 10 March 2008

### Re: What to look for

Welcome to this forum, Winelines

winelines wrote:the techniques that are "pattern-based", like X wing, turbo fish, swordfish, XYwing and also coloring. But, I am very slow to recognize the "chain- based" solutions. So far, the few I have found were after long sessions of trial and error.

I wouldn't say colouring is pattern based, although it is associated to a chain pattern.
A chain of a given type (xy, AIC, nrc, nrct,…) is as much pattern-like as the patterns you're citing. Unfortunately, this is too often hidden by the widespread confusion entailed by notions such as "chains of inference", "weak link" and so on, used when chains are discussed. When one speaks of a chain of inference, he is very likely to fall into the confusion between:
- a predefined chain pattern that gives rise to a predefined elimination,
- and an arbitrary sequence of rule applications that is needed before an elimination can be obtained (T&E).

winelines wrote:some hints, tricks or triggers that they use to recognize that "chain" techniques would be applicable to a particular puzzle.

Generally speaking, chain techniques are not only applicable but necessary whenever the puzzle is sufficiently hard. So, I'd say: when no elementary rule works, start looking for chains.
And, when looking for chains, start by looking for the simplest types, and then for types of increasing complexities (and for chains of increasing lengths).
But this is of course a personal preference and "elementary" will be given different meanings by different people.

winelines wrote:how they select where to try starting and ending the chain.

This is the difficult part of the question. I'd say there is "some" reason why we want to eliminate some candidate and we look for chains that could do so. But I think much works remains to be done on this general topic of focusing the search for chains.
Not only does your question make sense, but it is also an interesting one: whereas the chains patterns, like any other pattern, can be given purely logical descriptions and lead to well proven eliminations, i.e. they are in the realm of pure logic, the general topic of focusing the search will probably lead us into the realm of heuristics.
denis_berthier
2010 Supporter

Posts: 1377
Joined: 19 June 2007
Location: Paris

Thanks so much for your response, Denis.

Let me add a little to my rationale for the use of the term pattern-based, since I think I was speaking of it in a heuristic, not a logical sense. When I try to apply coloring, and filter on individual numbers, I generally find that 3 or 5 numbers are filled or contain only strong links, while a few others contain mostly numbers linked weakly. That generally only leaves 1- 3 numbers where coloring can be expected to yield positive results (reasonable combination of strong and weak links). In this case it is the pattern of the single numbers that lead me quickly to a solution (if there is one).

For me, the other common techniques require a similar recognition of a pattern. The XY wing is a little different because I understand that it is really a chain technique, however, filtering on pairs, makes it generally easy to spot. So in my mind, I look for a L pattern using the same three numbers.

Maybe if I were to be able to solve a suffient number of puzzles using X chain, XY chain, ALSs, I would "learn" what to look for. I gather that is what you meant by the application of heuristics. But right now I am flying blind.