Having trouble with this one

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Having trouble with this one

Postby PhilC » Fri Feb 24, 2006 3:45 pm

This is from Koalog's free sudoku of the day. Sudoku Susser couldn't find anything short of tabling.

Code: Select all
+-------+-------+-------+
| . . . | . . 5 | . . . |
| 9 2 8 | . . . | . . . |
| . . 4 | . 1 . | 2 3 . |
+-------+-------+-------+
| . . . | . . . | 5 . 2 |
| 4 . . | 8 . . | . . . |
| 8 1 . | . 2 3 | . 4 . |
+-------+-------+-------+
| 5 4 . | . . . | . . . |
| . . . | . 3 . | 6 . 7 |
| . . 9 | . 7 . | 4 . . |
+-------+-------+-------+


+--------------+------------------+------------------+
| 1    367  36 | 2     4689  5    | 789   679   469  |
| 9    2    8  | 3     46    467  | 17    1567  1456 |
| 67   5    4  | 679   1     6789 | 2     3     689  |
+--------------+------------------+------------------+
| 367  379  36 | 1479  49    149  | 5     8     2    |
| 4    79   2  | 8     5     679  | 1379  1679  1369 |
| 8    1    5  | 679   2     3    | 79    4     69   |
+--------------+------------------+------------------+
| 5    4    7  | 169   689   1269 | 1389  129   139  |
| 2    8    1  | 459   3     49   | 6     59    7    |
| 36   36   9  | 15    7     128  | 4     125   158  |
+--------------+------------------+------------------+


Any help appreciated!
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Postby Carcul » Fri Feb 24, 2006 4:19 pm

Hi PhilC.

First, let's notice that r3c1<>7 due to the Almost Unique Pattern in cells r1c2/r1c3/r4c1/r4c3/r9c1/r9c2 (if r3c1=7 then the puzzle would have more than one solution). After that, you only need a XY-Wing (to eliminate "9" from r3c9) to complete the puzzle.

Regards, Carcul
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Postby tarek » Fri Feb 24, 2006 4:28 pm

hi PhilC,

no simple technique............

My solver had to use forcing chains....... (simple though) to crack it

in total 21 non single moves
& 13 are advanced moves.

Tarek
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Postby Carcul » Fri Feb 24, 2006 4:33 pm

Hi Tarek.

Tarek wrote:no simple technique............


See my previous post for two simple steps.

Regards, Carcul
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Postby tarek » Fri Feb 24, 2006 4:43 pm

Carcul wrote:Hi Tarek.

Tarek wrote:no simple technique............


See my previous post for two simple steps.

Regards, Carcul


so you consider AUR as simple:D (How many people share that opinion !:D )

making a solution in 2 steps doesn't make it simple, however it is elegant & I think I should be implementing AUR in my solver........

After several stages in development, I think AUR is the last bit left to implement, I still haven't implementd simple colouring, but apparantly I don't need it anyway after finned fishes.

Tarek
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Postby PhilC » Fri Feb 24, 2006 8:49 pm

Thanks, Carcul.

So this is like the unique rectangle technique but with more cells. Cool.:D
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Postby ronk » Fri Feb 24, 2006 11:03 pm

Carcul wrote:let's notice that r3c1<>7 due to the Almost Unique Pattern in cells r1c2/r1c3/r4c1/r4c3/r9c1/r9c2 (if r3c1=7 then the puzzle would have more than one solution).

Great deduction, but I think the adjective Almost is incorrect. With the same sense of Unique as for the Unique Rectangle, what you describe is a Unique Swordfish.

Ron
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Postby Carcul » Sat Feb 25, 2006 11:10 am

Hi Ronk.

I think it would be Unique if it had only one "7": as the pattern has two "7s", I call it Almost Unique Pattern. But, if you prefer to call it another name, that's ok, but I will keep my own vocabulary.

Regards, Carcul
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Postby vidarino » Sat Feb 25, 2006 11:33 am

Carcul wrote:I think it would be Unique if it had only one "7": as the pattern has two "7s", I call it Almost Unique Pattern.


Hmm, I think I'm with ronk on this one. To me, a Unique Pattern simply means that it's not a BUG-Lite (or MUG-Lite), since if it was, it wouldn't be uniquely defined. (It wouldn't really have two solutions, though, since there is only one solution to the puzzle, but it would lead to a contradiction instead.)
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Postby Carcul » Sat Feb 25, 2006 11:52 am

Hi Vidarino.

I make a comparision between Unique Rectangles and these Unique Patterns: if such a pattern has a direct relationship with a Unique Rectangle (Type-1,2,3,4), then I call it an Unique Pattern; if the pattern is similar to an AUR, then I call it Almost Unique Pattern (in the sense that I have defined the various types of AURs). For example, in the present puzzle, if "7" is not in r1c2 then "7" must be in r4c1, and vice-versa: this way of thinking remind me an AUR. And if such a pattern has more extra candidates then a corresponding AUR, but still can be used in a deduction, then I call it Almost Almost Unique Pattern (or Rectangle, or Loop). I think the correspondence between rectangles, loops, and these patterns is obvious and logical, so I don't see where is the problem.

Regards, Carcul
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Postby vidarino » Sat Feb 25, 2006 12:01 pm

Hi Carcul.

Carcul wrote:I make a comparision between Unique Rectangles and these Unique Patterns: if such a pattern has a direct relationship with a Unique Rectangle (Type-1,2,3,4), then I call it an Unique Pattern.


Ah, but the Swordfish above *is* actually a type 2 Unique Pattern. (Or is it type 5? I'm not sure of the difference between these... One forms a straight line while the other does not, maybe?)

The 36-Swordfish has two extra 7s, one or more of which must be true, hence you can eliminate all other 7s that can see both of these. In this case, you can safely eliminate not just the one you pointed out (R3C1) but also R4C2 and R5C2. So this one fits type "type 2 (or 5)" description perfectly.:)

However, if you have a rectangle with corners 367 36 / 36 368 I would certainly agree to calling it an Almost Unique Pattern, since it doesn't lead to any reductions in itself, but only forms a link between the corners with extras. (If one isn't 7, the other must be 8 and vice versa.)

That's how I see it, anyway. Feel free to differ.:)

Vidar
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Postby ronk » Sat Feb 25, 2006 12:48 pm

vidarino wrote:Ah, but the Swordfish above *is* actually a type 2 Unique Pattern. (Or is it type 5? I'm not sure of the difference between these... One forms a straight line while the other does not, maybe?)
.....................
That's how I see it, anyway. Feel free to differ.:)

I agree.

Although I haven't yet seen an "official definition" similar to MadOverlord's collation for types 1 thru 4, several people seem to be using "type 5" for the pattern with the extra candidates on a diagonal. I'm happy with that.

Ron
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Re: Having trouble with this one

Postby mantouq » Sat Feb 25, 2006 6:14 pm

may i know how do u eliminate 6 from r4c456 and r5c2?

PhilC wrote:This is from Koalog's free sudoku of the day. Sudoku Susser couldn't find anything short of tabling.

Code: Select all
+-------+-------+-------+
| . . . | . . 5 | . . . |
| 9 2 8 | . . . | . . . |
| . . 4 | . 1 . | 2 3 . |
+-------+-------+-------+
| . . . | . . . | 5 . 2 |
| 4 . . | 8 . . | . . . |
| 8 1 . | . 2 3 | . 4 . |
+-------+-------+-------+
| 5 4 . | . . . | . . . |
| . . . | . 3 . | 6 . 7 |
| . . 9 | . 7 . | 4 . . |
+-------+-------+-------+


+--------------+------------------+------------------+
| 1    367  36 | 2     4689  5    | 789   679   469  |
| 9    2    8  | 3     46    467  | 17    1567  1456 |
| 67   5    4  | 679   1     6789 | 2     3     689  |
+--------------+------------------+------------------+
| 367  379  36 | 1479  49    149  | 5     8     2    |
| 4    79   2  | 8     5     679  | 1379  1679  1369 |
| 8    1    5  | 679   2     3    | 79    4     69   |
+--------------+------------------+------------------+
| 5    4    7  | 169   689   1269 | 1389  129   139  |
| 2    8    1  | 459   3     49   | 6     59    7    |
| 36   36   9  | 15    7     128  | 4     125   158  |
+--------------+------------------+------------------+


Any help appreciated!
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Re: Having trouble with this one

Postby mantouq » Sat Feb 25, 2006 6:27 pm

sorry i got it. it's xyz wing

mantouq wrote:may i know how do u eliminate 6 from r4c456 and r5c2?

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Postby ronk » Sun Feb 26, 2006 10:49 pm

Here's another one of those "thingies", aka BUG-Lite+2, aka Unique Swordfish, aka Almost Unique Pattern:
Code: Select all
 6..|2.8|7..
 ...|3..|...
 ...|...|.4.
 ---+---+---
 1..|...|..3
 ...|9..|2..
 54.|...|...
 ---+---+---
 .32|...|...
 ...|.5.|.1.
 ...|.4.|...


 6   5   4   | 2   9   8   | 7   3   1
 2   9   178 | 3   167 4   | 5  *68 *68
 3   78  178 | 5   167 67  | 9   4   2
-------------+-------------+------------
 1   2   9   | 4   678 5   |*68 *678 3
 78  678 678 | 9   3   1   | 2   5   4
 5   4   3   | 678 2   67  | 1   9   678
-------------+-------------+------------
 78  3   2   | 1   678 9   | 4   678 5
 4   678 678 | 78  5   2   | 3   1   9
 9   1   5   | 678 4   3   |*68  2  *678

According to the uniqueness principle, either r4c8=7 or r9c9=7. Therefore, candidates 7 which see both may be eliminated, i.e., r6c9<>7 and r7c8<>7.

Ron
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