## two "new" techniques, Skyscraper and 2-string Kite

Advanced methods and approaches for solving Sudoku puzzles

### two "new" techniques, Skyscraper and 2-string Kite

Hi.

I have been working a long time to try and find different patterns, and I thought I would present two of them on this forum.

I did discover that both of them can be classified under what is known as the "Turbot Fish", but I still think that someone might find them useful...

Skyscraper:
Code: Select all
`. . . | . . . | . . .* * . | . d . | . . .. . b | * | * | . . .----|-----|----------. . | | . | . | . . .. . | | . | . | . . .. . | | . | . | . . .----|-----|----------. . | | . | . | . . .. . | | . | . | . . .. . a | . c . | . . .`

if ab and cd are two strong links (Conjugate Pairs), if a and c are on the same line (row or column) and b and d are within the same "box-area" (or the same "chute" I think it is called?), then all candidates with the same number as abcd on these: * spots can be eliminated.
As you can see, this definition fits well with an image of a skyscraper

example puzzle that needs Skyscraper to solve:
Code: Select all
`. . 1 | 7 2 9 | . . .. . 6 | 8 3 1 | . 2 77 2 8 | 6 4 5 | 3 9 1---------------------. . . | 5 7 2 | 1 . 9. . 9 | . 6 . | 7 5 25 7 2 | 1 9 . | . 6 3---------------------. . 7 | 9 5 . | 2 1 8. . . | . 8 6 | . 7 4. . . | . 1 7 | . 3 .`

2-string Kite:
Code: Select all
`. . . | . . . | . . .. . c-----------d . .. a . | . . . | . . .--|------------------. | . | . . . | . . .. | . | . . . | . . .. | . | . . . | . . .--|------------------. b . | . . . | * . .. . . | . . . | . . .. . . | . . . | . . .`

if ab and cd are two strong links (Conjugate Pairs), and if a and c share the same box, then all candidates with the same number as abcd on this: * spot (where b and d meet) can be eliminated.
Here, the box that a and c shares is the "kite" and the two strong links are the "strings"

example puzzle that needs 2-string Kite to solve:
Code: Select all
`9 4 6 | 3 8 5 | 2 7 17 3 5 | 2 1 4 | 9 8 62 1 8 | 6 9 7 | 3 4 5---------------------3 9 1 | 8 7 6 | 5 2 4. . . | . 2 . | . 3 .. . 2 | . 3 . | . . 8---------------------1 6 . | . 4 3 | 8 5 2. . 3 | . 5 2 | . . .5 2 . | . 6 8 | . . 3`

I have incorporated both these patterns into my solver, so if you want to play around with them you can get it free at www.sudoku.frihost.net

Havard
Havard

Posts: 377
Joined: 25 December 2005

### Re: two "new" techniques, Skyscraper and 2-string

Havard wrote:I did discover that both of them can be classified under what is known as the "Turbot Fish", but I still think that someone might find them useful...

Hi Havard, welcome to the forum.
No offense intended, but I am wondering why new names are given to an existing technique which has so many different names already?
Jeff

Posts: 708
Joined: 01 August 2005

Thanks Jeff.

I guess I did not know they were called something else until I did some research, and found that they both can be called Turbot Fish. However I do think they have some advantage for "human solvers". At least the feedback I have got on them would suggest that they make the spotting of these patterns a lot easier. Not harder than finding an x-wing anyway.

Are there other names for these patterns as well?

Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard,

I can see your point, but this pattern can appear in many shapes that you would be very busy trying to give each one a different name. Other names for this pattern are turbot fish, fishy-cycle, multi-colouring, x-cycle, double chain, combination nice loop, advanced colouring, 3D-medusa, super-colouring and simple-colouring.

Turbot fish - This pattern was first identified by Nick70 and named due to one of its shape that looks like a fish. Each turbot fish consists of 5 cells. Anything with more than 5 cells, it is called a turbot chain.

Fishy-cycle - This term is being used in Susser to describe a turbot fish.

Multi-colouring - This term has been adopted in the Simple Sudoku solver by Angus. It covers the same pattern of 5 cells or more. This name can be confusing for newcomers since there are other kind of colourings, such as simple-colouring, advanced-colouring and super-colouring.

x-cycle - This term is being used in another forum and was introduced recently by Bob Hanson. An x-cycle can be of any length and repetitive or non-repetitive. I think this is the most meaningful amonst all; a cycle where all cells are linked by a single digit 'x'. It is compatible with an xy-chain where all cells are linked by 2 digits 'xy'. It is compatible with an x-wing which is just the shortest non-repetitive x-cycle of length 4.

Double chain - a turbot fish is just a special case of double implication forcing chains.

Combination nice loop - This is a term used to describe all double implication chains in a bilocation/bivalue plot, turbot fish included.

Advanced-colouring, Super-colouring and 3D-medusa are basically the same technique that combines x-cycle and xy-chain together. As such, they can be used to identify a turbot fish also.

Simple-colouring - Some people refer any colouring other than advanced colouring as simple-colouring which includes all turbot fish patterns.
Jeff

Posts: 708
Joined: 01 August 2005

Thanks for that summary! However, I would have to disagree that these are just two "random" names for "two-in-a-million" patterns, and I would like to show you why:

The Turbot Fish comes in many variations, with patterns using both two, three and four strong links. (five strong links is impossible as we know)
However, the only patterns that needs to be discovered are the ones with two strong links, because all the ones with three and four will (after identifying a two-link pattern within it) be left with a single candidate, which of course will be the first to go in the next round of solving.

These three patterns are:

Code: Select all
`1: (named "skyscraper"). . . | . . . | . . . * * . | . d . | . . . . . b | * | * | . . . ----|-----|---------- . . | | . | . | . . . . . | | . | . | . . . . . | | . | . | . . . ----|-----|---------- . . | | . | . | . . . . . | | . | . | . . . . . a | . c . | . . .2: (named "two-string kite"). . . | . . . | . . . . . c-----------d . . . a . | . . . | . . . --|------------------ . | . | . . . | . . . . | . | . . . | . . . . | . | . . . | . . . --|------------------ . b . | . . . | * . . . . . | . . . | . . . . . . | . . . | . . .3: (the real "fish" pattern). . . | . . . | c . . . . . | . . . | . \ .. a . | . . . | . . d --|------------------ . | . | . . . | . . . . | . | . . . | . . . . | . | . . . | . . . --|------------------ . b . | . . . | * . . . . . | . . . | . . . . . . | . . . | . . .`

If you now add the general X-Wing pattern, I think you have a complete list of all possible "candidate-eliminating" patterns you can make with two strong links. (unless you can prove me wrong, of course:) )

Moving on to patterns with three strong links (swordfish being the easiest), you would of course get some other variations, but my point is that learning these patterns (which is no harder than finding an x-wing) would greatly expand the capabilities of a human solver.

I would also be very interested in seeing one of these "unnamed" shapes!

Havard
Havard

Posts: 377
Joined: 25 December 2005

Hi Havard.

No mean to be offensive, but why do you keep giving new names to patterns that have already a name? Regarding your patterns with two strong links, they are all examples of Turbot Fishes: #2 and #3 are simple Turbot Fishes, and #1 is a grouped Turbot Fish. Imagine if now someone would want to give a different name to each Swordfish formation, for example. Please let's not complicate things even more.

Regards, Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Hi Carcul. No offense taken.

I discovered these patterns long before I knew anything about the Turbot Fish. However after I discovered that they were already covered by the definition of Turbot Fish, I have made sure to say this in every post I have made. Hence I don't understand your need to point this out again?

With that said, the names are created to help remember the pattern. The skyscraper looks like a skyscraper, with the same "base" and two "tops" with different, yet similar height. The 2-string kite looks like a kite (the box) with two strings attached running out of it. This has a massive advantage for human solvers compared to remember what a "grouped Turbot Fish" is. In my opinion this is making it easier to spot and understand, not more complicated. Making advanced sudokusolving available to a larger audience if you whish.

Havard
Havard

Posts: 377
Joined: 25 December 2005

Hi. Just throwing in my two norwegian øre here.

IMHO, adding new names for easily recognized patterns doesn't have to be such a terrible idea. We still call it XY-wing, even though it's just a short Forcing Chain, right? And X-Wing and Turbot Fish are just X-Cycles. Heck, even X-Cycles is a special case of Grouped X-Cycles, where all the groups are of size 1. ;)

It's probably really tough for a medium level (as compared to the levels of published puzzles) human solver to dive right into the definitions for X-Cycles, nice loops and generic Forcing Chains right off the bat. Having easily remembered and recognizable special cases makes the transition smoother, and perhaps the solver even discovers the general cases of the patterns himself when the time comes.

I do agree that showing some moderation is in order, though. It's certainly not necessary to name every single subset of a generic pattern. I don't really have an opinion whether this is the case here, though. I just felt like sharing my opinion.

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

Would there be an X-wing or turbot fish if we knew X-Cycles First ? if the answer is yes then I will agree with Vidarino.

Whatever the answer, a 5 cell pattern is already small for it to be divided into subgroups isn't it???

tarek

Posts: 2644
Joined: 05 January 2006

Hi Havard, Since I couldn't convince you, I better join you. Here are 2 interesting patterns that you may like to give names for.

Code: Select all
`. . . | . . . | . . . . d---------c | . . . . . . | . . . | . . . --------------------- . . . | . . b | . * . . . . | . / . | . . . . * . | a . . | . . . --------------------- . . . | . . . |  . . . . . | f---------g . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . c-------------d . .--------------------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------------- . b-----------------a. . . | . . . | . . . . . . | . . . | * . .`
Jeff

Posts: 708
Joined: 01 August 2005

Hi Jeff. I hope that is not sarcasm I am sensing, but I'll take you seriously!

Code: Select all
`. . . | . . . | . . . . d---------c | . . . . . . | . . . | . . . --------------------- . . . | . . b | . * . . . . | . / . | . . . . * . | a . . | . . . --------------------- . . . | . . . |  . . . . . | f---------g . . . . | . . . | . . . `

This one is just a double "fish" pattern (refered to as pattern 3 in my previous post, not named by me) The two fishes are: ab+cd and ab+fg

The other one is a skyscraper, but you can eliminate much more than your single star: (as shown in my previous post)
Code: Select all
`. . . | . . . | . . * . . . | . . . | . . * . c-------------d . . --------------------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------------- . b-----------------a . . . | . . . | * . . . . . | . . . | * . .`

so I'll need some other examples please!
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:.......so I'll need some other examples please!

No harm to have some fun. The second one doesn't look like a skyscraper, but rather a deep sea starfish. I will settle with a sideway skyscraper though.

I made these patterns up myself for the time being. Shall let you know when I find some real examples.
Jeff

Posts: 708
Joined: 01 August 2005

Great! Look forward to it!

I am having loads of fun!
Havard

Posts: 377
Joined: 25 December 2005

I suppose the only problem I have with it is that you call them "new" techniques when they are just specific examples (not even really techniques) derived from an existing and fairly well known technique. If you want to propose giving particular turbot fish patterns names, you should probably make your title reflect that.
Myth Jellies

Posts: 593
Joined: 19 September 2005

Hi MJ, you must be reading my mind. Personally, I find the names that Havard has given to the turbot fish configurations quite innovative.
Jeff

Posts: 708
Joined: 01 August 2005

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