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

Post puzzles for others to solve here.

Postby ravel » Sat Oct 07, 2006 12:13 pm

wapati wrote:There are: x-wing, xy-wing, xyz-wing, finned-x and Urs of 3 types in here.
No one application, or even two solves it, you need lots!
udosuk wrote: According to Simple Sudoku, you only need 2 x-wings plus 3 finned-x/turbot-fish/simple-color moves to solve it...
Actually, the remote pair [edit:] 48 (r7c6<>48) solves it immediately.
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Postby udosuk » Sat Oct 07, 2006 1:33 pm

ravel wrote:Actually, the remote pair [edit:] 48 (r7c6<>48) solves it immediately.

After singles, we're into this state:
Code: Select all
 *-----------------------------------------------------------*
 | 7     2     6     | 58    89    3     | 1     4     59    |
 | 1     8     3     | 7     4     59    | 2     59    6     |
 | 5     4     9     | 6     1     2     | 8     3     7     |
 |-------------------+-------------------+-------------------|
 | 3     59    2     | 1     6     7     | 4     59    8     |
 | 6     7     48    | 2     89    4589  | 3     1     59    |
 | 48    59    1     | 458   3     4589  | 6     7     2     |
 |-------------------+-------------------+-------------------|
 | 48    3     5     | 9     2     148   | 7     6     14    |
 | 2     1     7     | 34    5     6     | 9     8     34    |
 | 9     6     48    | 348   7     148   | 5     2     134   |
 *-----------------------------------------------------------*

I see... Remote pair {59} -> Remote pair {48} -> r7c6<>4|8
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Postby wapati » Sat Oct 07, 2006 1:47 pm

I hear you Ravel and udosuk

I do not see any eliminations from your text.

Please expand, I am confused.
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Postby Carcul » Sat Oct 07, 2006 2:05 pm

Here's what I see:

Code: Select all
 *-----------------------------------------------------*
 | 7     2     6  | 58    89    3    | 1     4     59  |
 | 1     8     3  | 7     4     59   | 2     59    6   |
 | 5     4     9  | 6     1     2    | 8     3     7   |
 |----------------+------------------+-----------------|
 | 3     59    2  | 1     6     7    | 4     59    8   |
 | 6     7     48 | 2     89    4589 | 3     1     59  |
 | 48    59    1  | 458   3     4589 | 6     7     2   |
 |----------------+------------------+-----------------|
 | 48    3     5  | 9     2     148  | 7     6     14  |
 | 2     1     7  | 34    5     6    | 9     8     34  |
 | 9     6     48 | 348   7     148  | 5     2     134 |
 *-----------------------------------------------------*

We have r7c6=1 or r5c6=5,9. But r5c6 cannot be 5,9 because of cells r2c68/r4c8/r5c9. So, r7c6=1 and the puzzle is solved.

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Postby ravel » Sat Oct 07, 2006 2:18 pm

Thanks for clarifying, udosek.
[edit:]And thanks for complicating, Carcul:)
Code: Select all
 *-----------------------------------------------------------*
 | 7     2     6     | 58    89    3     | 1     4    #59    |
 | 1     8     3     | 7     4    #59    | 2    #59    6     |
 | 5     4     9     | 6     1     2     | 8     3     7     |
 |-------------------+-------------------+-------------------|
 | 3     59    2     | 1     6     7     | 4     59    8     |
 | 6     7    @48    | 2     89   @4589  | 3     1    #59    |
 |@48    59    1     | 458   3     4589  | 6     7     2     |
 |-------------------+-------------------+-------------------|
 |@48    3     5     | 9     2    -148   | 7     6     14    |
 | 2     1     7     | 34    5     6     | 9     8     34    |
 | 9     6     48    | 348   7     148   | 5     2     134   |
 *-----------------------------------------------------------*
Wapati, remote pairs are easy to spot, probably easier than x(yz)-wings and UR's of type 3,4. You have a connected chain of cells containing 2 digits ab with an odd number of links. Then you can eliminate ab from the cells, that see the first and last cell of the chain. If n=3, you have something like a double turbot fish (2 strong links), where the eliminations can be done for both digits.
The first remote pair is with 59: r2c6-r2c8-r1c9-r5c9. (or r4c8 instead of r1c9)
r2c6=5 => r2c8=9 => r1c9=5 => r5c9=9
r2c6=9 => r2c8=5 => r1c9=9 => r5c9=5
So either r2c6=5 and r5c9=9 or r2c6=9 and r5c9=5 (one of the cells must be 5, the other 9)
Therefore r5c6 cannot be 5 or 9.

Same with 48 then in the cells marked with @ (or r9c3 instead of r7c1) => r7c6<>48.
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Postby wapati » Sat Oct 07, 2006 3:56 pm

Double remote pair seems to solve it. Wow!

It did seem a tangle!!
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Postby wapati » Wed Oct 11, 2006 5:13 am

Another that needs several bigger steps, again several paths.

Code: Select all
. . . | . 5 . | 6 . 8
2 . . | . . 6 | . . .
. . 7 | . 3 . | . . 4
---------------------
3 . . | . 4 7 | . 1 .
9 5 . | . 2 3 | 8 . 7
. . . | 9 . . | . . .
---------------------
. 1 4 | . . . | 7 . .
. . 5 | . 6 . | . . .
. . . | . 7 4 | . 9 .
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Postby Carcul » Wed Oct 11, 2006 9:57 am

Wapati wrote:Another that needs several bigger steps, again several paths.


Code: Select all
 *-------------------------------------------------------*
 | 1     34    9    | 47    5     2   | 6     37    8    |
 | 2     348   38   | 47    19    6   | 1359  357   1359 |
 | 5     6     7    | 18    3     189 | 19    2     4    |
 |------------------+-----------------+------------------|
 | 3     28    268  | 568   4     7   | 259   1     569  |
 | 9     5     16   | 16    2     3   | 8     4     7    |
 | 4     7     1268 | 9     18    158 | 235   356   356  |
 |------------------+-----------------+------------------|
 | 68    1     4    | 23    89    589 | 7     3568  2356 |
 | 7     9     5    | 23    6     18  | 4     38    123  |
 | 68    23    23   | 158   7     4   | 15    9     156  |
 *-------------------------------------------------------*

We have r9c4=1 or r4c4=6, and r9c4=1 or r3c6=1 or r4c4=8. But the first tell us that r4c4<>8, so r9c4=1 or r3c6=1, and so r8c6<>1. So, r8c6=8 and the puzzle is solved.

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Postby wapati » Thu Oct 12, 2006 3:53 pm

Here is one that needs a swordfish and then 3 (or 4) xys!

Code: Select all
8 7 .|4 . .|. . 2
. 9 .|. 8 .|3 . .
. 4 .|. . .|5 7 .
-----+-----+-----
. . .|1 . 5|. . .
4 . .|. . .|. 8 .
7 1 .|. . 2|. . 6
-----+-----+-----
. . .|. . .|. . .
5 . .|9 . .|8 4 7
. 3 .|7 1 .|. . 5
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Postby Carcul » Thu Oct 12, 2006 7:36 pm

Wapati wrote:Here is one that needs a swordfish and then 3 (or 4) xys!


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.

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Postby wapati » Fri Oct 13, 2006 4:33 am

I do not consider forcing chains.

A guess is just a guess.....
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Postby udosuk » Fri Oct 13, 2006 4:46 am

wapati wrote:I do not consider forcing chains.

A guess is just a guess.....

But xy-wings are just instances of forcing chains (with length 4)...

Forcing chains are different to guessing... You prove a certain candidate would lead to a contradiction, therefore you eliminate it... It's sound and solid logic, though not as elegant as the simpler moves...

For this puzzle, I prefer the swordfish+4 xy-wings route than the 6-cell forcing chain proposed by Carcul... Though it's just a matter of personal taste...
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Postby wapati » Fri Oct 13, 2006 5:08 am

udosuk wrote:
wapati wrote:I do not consider forcing chains.

A guess is just a guess.....

But xy-wings are just instances of forcing chains (with length 4)...

Forcing chains are different to guessing... You prove a certain candidate would lead to a contradiction, therefore you eliminate it... It's sound and solid logic, though not as elegant as the simpler moves...

For this puzzle, I prefer the swordfish+4 xy-wings route than the 6-cell forcing chain proposed by Carcul... Though it's just a matter of personal taste...


I see a pattern in x wings, swordfish and such.
I see the pattern, I use it.

Forcing chains, to me, seems to be that you start anywhere and zoom around until you find something.

It would be cool if forcing chains had a method, like ...
I dunno, a method for where to start, what number to work on, when to start.
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Postby udosuk » Fri Oct 13, 2006 6:42 am

Yeah, you're right about pattern-based techniques (i.e. fishes) "feels" more logical than forcing-chains type of moves (which involve looking at different candidates in different lines/boxes)... But my point is, since this particular puzzle requires xy-wings (and 4 of them), which are just the shortest types of forcing chains, you couldn't say "you don't consider forcing chains"... You just don't consider forcing chains of lengths more than 4...

And I wouldn't say Carcul's method isn't as logical as yours because you're both using forcing chains (of which you're not aware)... All I can say is I "feel" your method is a touch more elegant because it uses shorter forcing chains...

And to look for xy-wings you still need to "start anywhere and zoom around until you find something"...
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Postby Havard » Fri Oct 13, 2006 8:09 am

oh, I love this discussion! Can I join?:)

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)

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)

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