The New Sudoku Players' Forum

by **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.

by **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

by **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.

by **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.

Carcul

by **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.

by **wapati** » Sat Oct 07, 2006 3:56 pm

Double remote pair seems to solve it. Wow!

It did seem a tangle!!

by **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 .

by **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.

Carcul

by **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

by **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.

Carcul

by **wapati** » Fri Oct 13, 2006 4:33 am

I do not consider forcing chains.

A guess is just a guess.....

by **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...

by **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.

by **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"...

by **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)

Havard

The New Sudoku Players' Forum

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