## simple nice loops

Advanced methods and approaches for solving Sudoku puzzles

### simple nice loops

I've started playing with nice loops (and I've added them to my solver). A couple of the simplest nice loops are easy to spot and have their own names:
x-wings
Code: Select all
` . 1 . | . 1 . | . . .  . - . | . - . | . . .  . - . | . - . | . . .  ------+-------+------  . - . | . - . | . . .  . - . | . - . | . . .  . - . | . - . | . . .  ------+-------+------  . 1 . | . 1 . | . . .  . - . | . - . | . . .  . - . | . - . | . . . `

and a technique Ruud calls colour wing:
Code: Select all
` . . . | . . . | . . .  . . . | . . . | . . .  . . . | . . . | . . .  ------+-------+------  . . . | 1 . . | 1 - .  . . . | . . . | . - .  . . . | . . . | . - .  ------+-------+------  . . . | 1 . . | - 1 .  . . . | . . . | - . .  . . . | . . . | - . . `

There is a third of these simplest nice loops which is as easy/hard to spot as the other two, but I don't think it has a special name. If not I propose that it's called a v-wing, for obvious reasons. It only leads to elimination in one cell, so may be of limited use, but it's closely related to the simplest colour trap, which is useful!
Code: Select all
` . . . | . . . | . . .  - . . | . 1 . | . . .  . . . | . . . | . . .  ------+-------+------  . . . | # 1 # | . . .  1 . . | 1 . . | . . .  . . . | # . # | . . .  ------+-------+------  . . . | . . . | . . .  . . . | . . . | . . .  . . . | . . . | . . .`

The cells marked # can be the candidate, in this case 1, without affecting the elimination. If the cells marked # do not contain the candidate, then the formation is a simple colour trap.
ab
ab

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Joined: 06 September 2005

### Re: simple nice loops

Last edited by ronk on Thu Dec 14, 2006 6:06 pm, edited 1 time in total.
ronk
2012 Supporter

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Ab wrote:but I don't think it has a special name.

It has two: Turbot Fish and Nice Loop. I hope you are not going to name every possible combination of strong/weak links.

Ab wrote:and a technique Ruud calls colour wing:

Never heard of. Its simply another example of a Turbot Fish. I keep thinking that you people are complicating things by giving different names to the same thing.

Carcul
Carcul

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Joined: 04 November 2005

thanks for the info Carcul. I don't intend to name every example of nice loops, as you say they already have a name. However I think it's useful for some easy examples to have a name as that helps people to learn to use the technique. Clearly I am not alone in this thought as someone else has already decided to call these examples Turbot fishes!
ab
ab

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Joined: 06 September 2005

Ab wrote:Clearly I am not alone in this thought as someone else has already decided to call these examples Turbot fishes!

That someone was Nick70. And in the time he named those patterns the concept of Nice Loop wasn't even known. Later it was showed that X-Wings, Swordfishes, Turbot Fishes, and Colors were all particular cases of Nice Loops, a much more "grasping" concept.

Ab wrote:However I think it's useful for some easy examples to have a name as that helps people to learn to use the technique.

I cannot see how, but if you say so, then ok.

Carcul
Carcul

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Carcul wrote:Later it was showed that X-Wings, Swordfishes, Turbot Fishes, and Colors were all particular cases of Nice Loops, a much more "grasping" concept.
I dont see that for Swordfish (or xwing directly). Of course you can write a Nice Loop that eliminates any candidate, that can be eliminated by a Swordfish (when you allow x-wing or a nested loop in your deduction), but how would you formulate a single Nice Loop, that eliminates all of them without subsub loops ? When you say (in the extreme), that nested loops are allowed for any depth, you can just take the output of a try/error solver with only singles implemented and formulate it as a Nice Loop (there are sudokus that need more than 1000 "nodes" or "if thens"), but such a solution is of course valid, but not readable.
ravel

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i think it's just swordfish with two candidates in each line that are nice loops, not all of them. Likewise jellyfish.

x-wings are nice loops. if the x-wing cosists of the candidate appearing in just 2 columns in 2 rows as in my example above, then the strong links are in the rows and the weak links are in the columns.

ab
ab

Posts: 451
Joined: 06 September 2005

Code: Select all
` . 1 . | . 1 . | . . . . - . | . - . | . . . . - . | . - . | . . . ------+-------+------ . - . | . - . | . . . . - . | . - . | . . . . - . | . - . | . . . ------+-------+------ . 1 . | . 1 . | . . . . - . | . - . | . . . . - . | . - . | . . .`
Lets look at your example: i see 2 loops, but not one for all:
[r2345689c2]-1-[r1c1]=1=[r1c5]-1-[r7c5]=1=[r7c1]-1-[r2345689c2]
r[2345689c5]-1-[r1c5]=1=[r1c1]-1-[r7c1]=1=[r7c5]-1-[r2345689c5]
ravel

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Joined: 21 February 2006

Hi ab,

You should have a look at this post from Havard :

www.sudoku.com/boards/viewtopic.php?t=3326

and the extensions in that one :

www.sudoku.com/boards/viewtopic.php?t=3438

Mage
Mage

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Location: France

ravel, an x-wing is a single continuous loop as well as 2 discontinuous loops.

[r1c1]=1=[r1c5]-1-[r7c5]=1=[r7c1]-1-[r1c1]
Myth Jellies

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