## Simple Sudoku

Advanced methods and approaches for solving Sudoku puzzles

### Simple Sudoku

I am following this forum for a couple of months now and I think I have an idea of the most techniques (not of all details, not the real big fishes with various fins or the wxyz-ALS rules). Sometimes I understand these too (after explanations), but I am almost never able to spot them by my own. All the same I solve most of the puzzles, even some of the really difficult ones. These are my "house-made" techniques which may be not very elegant but which give surprisingly often some useful eliminations.

1. Basic techniques (including [hidden] pairs and triples, blocked candidates, X-wing, Swordfish, coloring and xy-wing [often difficult to spot]), in short: as far as Simple Sudoku comes.

2. Beyond Simple Sudoku I look for Empty Rectangles (mostly already done by multi-coloring), AURs, xyz-wings, remote pairs or - eventually - a BUG pattern.

3. If these techniques don't solve the puzzle I look for contradictions. Generally I begin with a "promising pair" in a "base-cell". A promising pair is often a unique pair on the grid which contains one candidate of which there are only a few left (maybe only in two or three boxes) and one "power-candidate" (you find everywhere on the grid). If the first candidate in the base cell (for example "a") leads to an elimination of the other one ("b") in a cell which is seen by the base cell, you can eliminate this "b" (if the base cell contains a "b", it would be eliminated anyway).

4. If that does not lead to any elimination I try the (here so called) a-b-c technique. I choose a triple and look what happens if one of the candidates was not in the cell. If the cell contains "abc" and "ab" leads to "a" then "b" can be eliminated. (If the "right candidate" is "c", "b" cannot be correct either). This works often if the chosen cell leads to some eliminations due to an AUR.

5. If that does not work I give up.

Some will argue this is pure "trial and error" (which would not bother me very much), but I don't see any really substantial difference to the nice loop and ALS techniques for instance. In my opinion any (advanced or not advanced) technique works on the principle that you exclude candidates by imagening how the grid could be filled. Example: a finned X-wing only works because you can make the following deduction: If the fin-candidate is wrong you can eliminate the candidate in the same box (by the X-wing rule). If the fin cell is right the same elimination can be done, because the fin cell contains "the" candidate and is in the same box. I don't believe in the fundamental distinction between "seeing a pattern"(good) or "observing cause and effect" (bad).

Neunmalneun

Posts: 52
Joined: 22 December 2005

Hi Neunmalneun,

just interesting, it seems, that we use about the same order of techniques. I would add URs and BUG+1 (which only appears at the end of the game) to the basics.
Also ER's are very easy to spot: if you have a strong link in a row (column) over 2 boxes, you can see immediately, if there is an ER in the corresponding boxes above/below (left/right). But they are rather rare compared to say turbot fishes.

If i understand it right, in point 3 you are describing, how you look for xy-chains. I did not distinguish between more or less "promising" starting cells so far. I start here and there and try to keep in mind things like "a 4 here leads to a 5 there", what might help for another try. [Edit: i forgot: often i get a contradicton rather than an xy-chain, also fine]

Point 4 is quite interesting. I remember, that i have seen such a deduction from you, but i think, i never did it this way myself.

Point 5: Of course i never give up, i only make a break for an indefinite time

If i am very anxious for solving the puzzle, next i go through the strong links and try to get a contradiction for the number in either of the cells. This is cumbersome, but if i have success, it will give me a number.

Concerning the ALS: I never found one, when i looked for one. But i found some "accidently", when i used tuples in chains.
ravel

Posts: 998
Joined: 21 February 2006