## Complete Sudoku Solving Techniques

Advanced methods and approaches for solving Sudoku puzzles

### Complete Sudoku Solving Techniques

Hi..
In one of the post i just came across names of these techniques and the proper follow through of this techs while solving Sudoku.
90% of these techs are unknown to me and i guess may be unknown to any newbie here. So may be any techie or anybody having clear concepts of these may post the method and use of these techniques while solving sudoku.

This would be helpful to Newbies and moderator can keep it sticky so that any newbie on this forum may refer to it.

There are many other websites having tips and methods for solving Sudoku but none of these have complete list so its getting tough to search for every website. And even some websites have wrongly defined some methods so to avoid confusion our forum member can contribute.

This will act as Tutorial and Methods for Solving Sudoku..Anybody willing to put in any efforts is highly appreciated

Pinned Squares 0
Simple Locked Sets 1
Simple Hidden Sets
Intersection Removal
Remote Locked Pairs
Comprehensive Locked Sets
Comprehensive Hidden Sets
Simple X-Wing
Swordfish
Jellyfish
Squirmbag
XY-Wing
XYZ-Wing
Uniqueness
Forcing Chains
Fishy Cycles
Nishio
Trebor's Tables
Bowman Bingo

Hope someone takes initiative.. Thanx..

Dipen
dipen01

Posts: 15
Joined: 26 September 2005

The post you refer to was written by Sudoku expert MadOverlord.
He has created an excellent Sudoku program called Sudoku Susser
(which is all the more impressive considering the time-consuming nature of
his main activity: world domination!). A nice feature is the accompanying manual,
which describes all of the techniques in this list.

Nick67

Posts: 113
Joined: 24 August 2007

Well..

Nick ..thanx for ur help regarding Sudoku Susser...

I was wondering if someone would write it with proper examples and priorities and usage coz then it would be helpful to other forum members.

As the other references you mentioned though are good but not as explainative.
dipen01

Posts: 15
Joined: 26 September 2005

dipen01 wrote:I was wondering if someone would write it with proper examples and priorities and usage coz then it would be helpful to other forum members.

Unlikely, the combined explanations would be colossal, they've been covered numerous times before (apart from the seriously esoteric ones, and you won't need those much) and to be honest - what's wrong with doing a bit of homework?

dipen01 wrote:As the other references you mentioned though are good but not as explainative.

Folk tend to find angusj's easier to access which is a bit of a shame for Sadman as any such site should be applauded. Maybe it's his Yorkshire brogue.

P.S. As to priorities and usage, the only helpful advice would be go with what you see when you see it. Some prefer to find singles, then pairs and so on. Personally I prefer to find the slightly harder locked candidates earlier on, because I can always find the easier stuff later. The point is: whatever you find, you'll affect other constructs which may/may not have been even more helpful.

P.P.S. Had you requested hot links to good expo's, I'd have definitely been on board. I suggested the same thing myself a few months back, to no avail. I'd bet my house that no-one is going to put effort into explaining what's already out there, but linking to it - that's another matter.
Karyobin

Posts: 396
Joined: 18 June 2005

I'd bet my house that no-one is going to put effort into explaining what's already out there

Now, if you'd said 'I'd bet the contents of my fridge' I'd believe you.

It really is time though that an updated and clear 'gazeteer' was available - Angusj's and Simes's sites are super although there's certainly room for one with a bit of interactive content. I might even do it myself - but my own fridge beckons rather too often. We'll see.

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

Mind you not all of those terms are widely used. What MadOverlord refers to as locked sets are better known as naked subsets, and hidden subsets are their counterpart. "Comprehensive" sets are just bigger subsets, and most solvers don't bother to give that a different name. Pinned squares are better known as hidden singles, and forced squares are better known as naked singles. Intersection removal goes by a number of names, and is often referred to as "pointing pairs" and "box-line intersections", which are really just two sides of the same coin.

Jellyfish and squirmbag are just 4x4 and 5x5 variants of swordfish, respectively; squirmbag will never appear in a 9x9 puzzle without finding something simpler first.

Fishy cycles is a technique which is a subset of complete simple coloring. Coloring isn't yet supported in the Susser.

Uniqueness is a family of tests that MadOverlord is currently working on implementing now. From recent correspondence he's planning to implement at least the first three variants, and has illuminated that the 3rd form of the test isn't as limited as I once thought. There are four variants overall, and forms 2-4 also have a "B" format. The logic for uniqueness is based on the fact that a valid sudoku must not have multiple solutions, so it is impossible for certain configurations to occur.

Bowman Bingo is kind of a human-doable trial-and-error. Another technique I'd recommend learning is bifurcating implication chains.
Lummox JR

Posts: 125
Joined: 22 September 2005

You'd have to be quite careful implementing the uniqueness test in a solver, wouldn't you? Since it relies on the solution being unique, which it might not be, so you'd effectively have to solve the puzzle before you could use it. By the by, has anyone yet settled whether you could use the uniqueness test to "fool yourself" into thinking there is a unique solution to a puzzle where there are really multiple?
PaulIQ164

Posts: 533
Joined: 16 July 2005

Paul - I reckon this one comes down to semantics - if I decide to use a uniqueness test it's because I've already recognised that a grid has multiple solutions and want to find at least one of them. Happy to discuss!

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

If a grid has multiple solutions, couldn't the uniqueness test get you in some trouble if you apply it? Might it then have no solutions at all?
PaulIQ164

Posts: 533
Joined: 16 July 2005

Indeed, the uniqueness test will not pick a solution out of a set of multiples, but will either narrow it down to a smaller multi-solution set or render the puzzle unsolvable. I don't think it's at all possible for the uniqueness test to reduce a multi-solution grid to one solution; if it doesn't lead to immediate contradiction it can only break a different unavoidable set. But then, who cares? If the puzzle had multiple solutions, it was invalid right from the beginning.

In a solver there should be no cause for worry. A program that assists people in solving should be checking the puzzle for validity any time a value is picked or a candidate from the solution is removed, or any time an invalid puzzle is changed or a puzzle is loaded for the first time. A program that is merely rating difficulty should have already verified the puzzle's uniqueness via something like DLX. The test should not be used, however, for setting the grid in the first place.
Lummox JR

Posts: 125
Joined: 22 September 2005

Well if some people have no idea what this magic sudoku is then; its the one in which only 9 clues are given.

I mean only one clue in each block and that too all clues are different so am in dilemma now that how to approach these kinda sudoku.

Any idea is appreciated !!
dipen01

Posts: 15
Joined: 26 September 2005

Well i guess i will need to start a new topic ..coz no one is replyin..here
dipen01

Posts: 15
Joined: 26 September 2005

I had a look but I couldn't understand the instructions.
Code: Select all
`There is some special rows (filled with blue color). The value of the numbers who are in this cells is lower or equal as the number of coloured cells in every quadrant. `

PS : OK I had another look. I get it.

PPS : I got the instructions but I can only get so far with the puzzle. Do you have to guess?
emm

Posts: 987
Joined: 02 July 2005

Well.. i got the method to solve that so called magic sudoku... All we have to do is randomly fill the starting 5-4 blocks and then we can arrange or manipulate other blocks so as to suit the given clues.. In this way i completed nearly 5 puzzles.. It takes very less time....
dipen01

Posts: 15
Joined: 26 September 2005

Well...

The idea is that: for each block (3x3 area), the blue squares all have a value less than or equal to teh number of blue squares in that block. For example, in todays' problem (#87), the top-left block has 7 blue cells in it, so they hold the numbers 1-7 (the 7 is already in place) and the white cells hold the 8 and 9.

Hope this helps.
Lardarse

Posts: 106
Joined: 01 July 2005

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