## Fun puzzle. So many methods to solve. No CHAINS required.

Post puzzles for others to solve here.
but for the record:
Carcul's:
Code: Select all
`[*------------------------------------------------------------* | 8      7      356 | 4      356    136  | 169    169    2   | | 12     9      256 | 256    8      7    | 3      16     4   | | 123    4      236 | 236    2369   1369 | 5      7      8   | |-------------------+--------------------+-------------------| | 236    26     8   | 1      4      5    | 7      239    39  | | 4      5      239 | 36     7      369  | 12     8      13  | | 7      1      39  | 8      39     2    | 4      5      6   | |-------------------+--------------------+-------------------| | 269    8      7   | 256    256    4    | 1269   12369  139 | | 5      26     1   | 9      236    36   | 8      4      7   | | 269    3      4   | 7      1      8    | 269    269    5   | *------------------------------------------------------------*[r6c3]=9=[r6c5]-9-[r5c6]=9=[r3c6]=1=[r3c1]=3=[r4c1]-3-[r6c3],and so r6c3<>3 which solves the puzzle.`

I don't think of as a forcing chain, rather a beautiful Nice Loop which in my opinion is as pattern as it gets.
Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:I would argue that an making a forcing chain out of a XY-wing is to degenerate the pattern, and will only ever account for 1 of the XY-wings 5 possible eliminations. (you would have to write 5 forcing chains for what the pattern XY-wing would do in one swoop)

All 5 exclusions may be put in one forcing chain expression:
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` .  .  .  | .  .  . *  xy *  | .  yz . xz .  .  | *  *  * [r2c23,r3c456]-z-r3c1-x-r2c2-y-r2c5-z-[r2c23,r3c456]`

Some people don't even include the discontinuity and would simply write ... r3c1-x-r2c2-y-r2c5 ... which is a bit too terse for me. I prefer to see the exclusions in the expression.

Havard wrote:I don't think of as a forcing chain, rather a beautiful Nice Loop ...

To me that's a distinction without a difference ... so I apparently don't know what a forcing chain is.
ronk
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I guess it is all about definition. When I say "forcing chain", I think of the sudoku-logic that goes: "if I put this number in here, then this will happen". I see Carculs Nice Loop as several strong links(patterns) put together following a set of predefined rules, where the elimination follows from those rules. Now you could of course also see it as a forcing chain, reading it as "if I put a 3 in [r6c3] then [r6c5] has to be a 9 etc.", but to me this is not the same thing. I see exactly the same relationship between a Forcing Chain and a Nice Loop as it is between Nishio and complex fish-patterns / x-cycles. Nishio will always be able to tell you what candidate can be removed, but the fish-patterns/x-cycles will be able to show you the underlying logic of the removal.
Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:oh, I love this discussion! Can I join?

Welcome on board!

Havard wrote:My view on this matter is best expressed in a post a wrote here a while back: http://sudoku.frihost.net/forum/viewtopic.php?t=920 (4th down)

Very in depth view... I also had a strong disliking about forcing chains before I encountered some of the most diabolical puzzles which cannot be solved otherwise... I guess one way to distinguish good and bad chains are the length... Those with 8-10 cells or more are definitely touching on trial & error...

Havard wrote:I would argue that an making a forcing chain out of a XY-wing is to degenerate the pattern, and will only ever account for 1 of the XY-wings 5 possible eliminations. (you would have to write 5 forcing chains for what the pattern XY-wing would do in one swoop)

Strictly speaking, XY-wing is just a special application of the "Almost Locked Set" technique... So I guess I wasn't technically correct when I said an XY-wing is the same as a forcing chain of length 4 (although all XY-wings could be rewritten as forcing chains like ronk has demonstrated)...

I have a peculiar definition about "patterns" which I don't expect many would agree... To me, there are 4 different classes of techniques:

Class 1: One number, one unit
This focuses on the appearance of one particular number (out of 9) on each of the 27 constraints (9 rows, 9 columns, 9 boxes) and 81 cells.

Examples: hidden singles, naked singles

Class 2: Multiple numbers, one unit
Here we inspect the behaviour of all 9 numbers on each of the 27 constraints... Basically, from the stand point of a program, it just scan all 27 constraints one by one and look for possible patterns.

Examples: hidden subsets, naked subsets

Class 3: One number, multiple units
Here we look at how a certain number is distributed (as candidates) on the whole grid, and see if some candidates could be eliminated. As a program, it just filter in a certain number and analyse the shape of the possible cells, with the other 8 numbers totally ignored.

Examples: locked candidates, x-wings (and bigger fishes), finned fishes, turbot fish/strong links, coloring/multi-coloring

Class 4: Multiple numbers, multiple units
These are the hardest to spot (both for players and programs)... You have to look through all possible units and the distributions of all candidates to work out any deduction/elimination...

Examples: xy-wings (and bigger ALSs), URs (and unique loops), remote pairs, BUGs, forcing chains...

To me, techniques in class 1 to 3 are "pattern-based", the class 4 ones are not... Which is why I regard xy-wings as (almost) equivalent to forcing chains...
udosuk

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Joined: 17 July 2005

I was hoping for some answer from Carcul that I could understand.

I am seeing that some people can come up with one chain that solves the puzzles I am posting, and these are puzzles that to me take several distinct steps.

What I was hoping to learn is whether there is a practical way to find that critical chain quickly?

Is it possible to find such a critical chain in every puzzle?

On a more petty level, is there "something" that prompts you to start on a particular number and square?
wapati
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wapati wrote:What I was hoping to learn is whether there is a practical way to find that critical chain quickly?
Talent and practice. like in real life
Is it possible to find such a critical chain in every puzzle?
For the hardest you need more of them.
On a more petty level, is there "something" that prompts you to start on a particular number and square?
On the one hand "almost patterns" that you can try to use. On the other, you would first concentrate on either/or numbers (i.e. numbers in bivalue cells and conjugated pairs) to start a chain.
ravel

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Havard in SA forum wrote:I must admit that I have a softer spot for the forcing chains that does not try out the same candidate that ends up being eliminated. By this I mean that if you have one BIVALUE cell (cell with only two candidates), and you "try" to see what happens if you make both of them TRUE, and you end up finding that no matter which one you set TRUE, somewhere else on the board a candidate has to be either TRUE or FALSE. The forcing chain I outright dislike are the ones where by setting a candidate to either true or false, you end up with a contradiction of some sort, and hence that candidate can be removed / placed. The reason for this is that there will almost always be a reason for this elimination that then completly escapes the solver. In other words, the logic that causes this will be completlely lost.

Interesting restriction on using a BIVALUE cell and a Forcing Chain to find commonly affected cells. This mirrors my love for Double Implication Chains (DIC) where BILOCATION cells for a value are used to find commonly affected cells. It's a great way to explain 95+% of my Templates eliminations without having to find finned fish -- which I'm terrible at locating.

Note: Most of the time, I have Forcing Chains/Nets disabled. They usually clutter up the solution by making it longer without any real contribution to very hard puzzles.
daj95376
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Wapati wrote:I am seeing that some people can come up with one chain that solves the puzzles I am posting, and these are puzzles that to me take several distinct steps.

That doesn't mean they are not interesting to solve.

Wapati wrote:I was hoping for some answer from Carcul that I could understand.

A Nice Loop is a very different thing from a guess. The only way to understand this is to solve many puzzles by hand, without any help from a computer. Then, if you get the essence of Nice Loops, you will eventually gladly keep using them in solving puzzles. If not, you will eventually keep saying that there is no difference between a Nice Loop and trial and error (or a guess).
For a start, check this classic post from Jeff, and the puzzle posted there as an exercise. In this post, I have presented some puzzles as additional exercises.

Carcul
Carcul

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Joined: 04 November 2005

Carcul wrote:That doesn't mean they are not interesting to solve.

That is good to know. Is there a puzzle type (eg BUG) where forcing chains are just the long way around?

Here is a puzzle! I use UR, xy, swordfish and BUG, in some order.
I am aware of an xyz that an xy can sort-of handle. FUN

Code: Select all
`. 5 . | . . . | . . 1. . . | 9 2 . | . . .6 9 . | . . 8 | 2 . .---------------------8 . . | . 1 5 | 4 . .1 . . | 6 . 2 | . 9 .. . . | . 7 . | . 1 .---------------------. . 6 | . . . | . . .. 4 . | . . . | 1 . 53 . . | . 4 6 | 8 . .`
wapati
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Location: Brampton, Ontario, Canada

Easier than that last one, just a bit. Similar in another way, try it and see?

Code: Select all
`7 . . | 1 . 2 | . . 6. . . | . . . | 7 . .. . . | . . . | 9 1 2---------------------9 . . | . 3 . | 6 . .. . . | 5 2 . | . . .6 . . | . . 7 | . . 4---------------------. 3 1 | 8 . . | 5 4 .. . 4 | . . . | 8 . .8 . 7 | . . 5 | . . 1`
wapati
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Location: Brampton, Ontario, Canada

udosuk wrote:
Class 3: One number, multiple units
Here we look at how a certain number is distributed (as candidates) on the whole grid, and see if some candidates could be eliminated. As a program, it just filter in a certain number and analyse the shape of the possible cells, with the other 8 numbers totally ignored.

Examples: ...,coloring/multi-coloring

Class 4: Multiple numbers, multiple units
These are the hardest to spot (both for players and programs)... You have to look through all possible units and the distributions of all candidates to work out any deduction/elimination...

Examples: ..., remote pairs, ...

To me, techniques in class 1 to 3 are "pattern-based", the class 4 ones are not... Which is why I regard xy-wings as (almost) equivalent to forcing chains...

changing the subject slightly, remote pairs is really class 3 because you could think of it as simple colours on two separate digits. ie if you have a remote pair on 3 and 4 it's also colouring on 3 and colouring on 4.
ab

Posts: 451
Joined: 06 September 2005

ab wrote:changing the subject slightly, remote pairs is really class 3 because you could think of it as simple colours on two separate digits. ie if you have a remote pair on 3 and 4 it's also colouring on 3 and colouring on 4.

Perhaps true, I have not ever used or learned colours.
Grouped x-wing handles all things that colours solve, so far for me.
Given that I don't know colours, I'd leave remote pairs in Class 4.

This thing takes me 4 big steps, sometimes 5. Am I missing a shortcut?
Code: Select all
`. . . | . 5 . | . . 22 8 . | . . 7 | . . .5 . 7 | 1 4 . | 3 . .---------------------. . . | . 3 . | . 1 .8 . 3 | . . 1 | 4 . 5. . . | 6 . . | 7 . .---------------------. . 5 | . 9 . | 8 . .7 . . | . . . | . 3 .. 4 . | . 1 . | 5 2 .`
wapati
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Location: Brampton, Ontario, Canada

ab wrote:changing the subject slightly, remote pairs is really class 3 because you could think of it as simple colours on two separate digits. ie if you have a remote pair on 3 and 4 it's also colouring on 3 and colouring on 4.

So remote pair is in fact 2 separate colouring moves... I don't use it much so I didn't know about that... Thanks for the info!
udosuk

Posts: 2698
Joined: 17 July 2005

When you solve puzzles on paper and only note pairs as pencilmarks before you need more, a remote pair will jump into your eyes before any coloring.
Then in most cases you will detect them before naked triples.
ravel

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Joined: 21 February 2006

'Nother one that takes me several big steps.

Code: Select all
`. 9 . | 2 . . | 1 4 .. 8 . | . 3 4 | . 2 5. 4 3 | . . 1 | . . 8---------------------1 . . | . . 3 | 8 6 .. . . | . 6 . | . 5 .6 . . | 1 . . | . . 7---------------------. . . | . . . | 4 . .. 1 . | . . . | 5 8 2. . . | 3 . 2 | . . .`
wapati
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Location: Brampton, Ontario, Canada

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