dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Set H Puzzle 17
Goto page 1, 2  Next
 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Puzzles by daj
View previous topic :: View next topic  
Author Message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Dec 23, 2008 4:14 am    Post subject: Set H Puzzle 17 Reply with quote

This puzzle just keeps on giving!

Besides presenting a difficult traditional solution, it can be cracked with any of the following:

1) Either of 2x W-Wings
2) A monster M-Wing
3) An XY-Wing extended to a 5-cell XY-Chain

Heck, there may even be URs that I didn't catch.

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

Play this puzzle online at the Daily Sudoku site

BTW: There are M-Wings and W-Wings that don't crack the puzzle! Very Happy
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Tue Dec 23, 2008 5:20 am    Post subject: Reply with quote

Maybe I made a lucky mistake, but it solved with one UR. I'll wait and see what others say before trying it again.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Tue Dec 23, 2008 7:04 am    Post subject: Reply with quote

After basics:

Code:
+----------------+----------------+----------------+
| 5    4    29   | 13   289  89   | 13   6    7    |
| 19   8    3    | 7    6    5    | 4    19   2    |
| 129  6    7    | 4    239  19   | 5    189  38   |
+----------------+----------------+----------------+
| 2368 12   126  | 5    38   7    | 9    18   4    |
| 389  5    19   | 136  4    189  | 7    2    368  |
| 389  7    4    | 136  389  2    | 13   5    368  |
+----------------+----------------+----------------+
| 26   12   126  | 9    7    3    | 8    4    5    |
| 7    9    8    | 2    5    4    | 6    3    1    |
| 4    3    5    | 8    1    6    | 2    7    9    |
+----------------+----------------+----------------+


The <13> rectangle is across four blocks and is not a UR. Not a way to get lucky, because <6> in R6C4 is incorrect.

Quote:
According to Sudoku Susser, it takes 1 X-wing and four XY-wings.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Tue Dec 23, 2008 7:27 am    Post subject: Reply with quote

keith wrote:
After basics:

Code:
+----------------+----------------+----------------+
| 5    4    29   | 13c  289  89   | 13d  6    7    |
| 19   8    3    | 7    6    5    | 4    19   2    |
| 129  6    7    | 4    239b 19   | 5    189f 38e  |
+----------------+----------------+----------------+
| 2368 12   126  | 5    38a  7    | 9   1-8   4    |
| 389  5    19   | 136  4    189  | 7    2    368  |
| 389  7    4    | 136  389  2    | 13   5    368  |
+----------------+----------------+----------------+
| 26   12   126  | 9    7    3    | 8    4    5    |
| 7    9    8    | 2    5    4    | 6    3    1    |
| 4    3    5    | 8    1    6    | 2    7    9    |
+----------------+----------------+----------------+

Following <3> through abcde shows the implication that if a is <3>, e is also <3>. Strong link ef on <8>. af is an M-wing with pincers <8>. Solving R4C8 and the puzzle. Laughing

Danny, is this your "monster M-wing"? (Actually, this ia a half M-wing.)

Edit: a and e are also a W-wing, strong link <8> in C8. Taking out <3> in b, also solving the puzzzle.

Keith


Last edited by keith on Wed Dec 24, 2008 12:34 am; edited 1 time in total
Back to top
View user's profile Send private message
Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Dec 23, 2008 8:08 am    Post subject: Reply with quote

If r4c1 is 26, a 126 Deadly Pattern results in r47c123. (Note that this would make r1c3=2.) Thus, r4c1 is 38, which solves the puzzle.
Back to top
View user's profile Send private message Visit poster's website
Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Tue Dec 23, 2008 4:50 pm    Post subject: Reply with quote

keith wrote:
After basics:

Code:
+----------------+----------------+----------------+
| 5    4    29   | 13   289  89   | 13   6    7    |
| 19   8    3    | 7    6    5    | 4    19   2    |
| 129  6    7    | 4    239  19   | 5    189  38   |
+----------------+----------------+----------------+
| 2368 12   126  | 5    38   7    | 9    18   4    |
| 389  5    19   | 136  4    189  | 7    2    368  |
| 389  7    4    | 136  389  2    | 13   5    368  |
+----------------+----------------+----------------+
| 26   12   126  | 9    7    3    | 8    4    5    |
| 7    9    8    | 2    5    4    | 6    3    1    |
| 4    3    5    | 8    1    6    | 2    7    9    |
+----------------+----------------+----------------+


The <13> rectangle is across four blocks and is not a UR. Not a way to get lucky, because <6> in R6C4 is incorrect.

Quote:
According to Sudoku Susser, it takes 1 X-wing and four XY-wings.

In boxes 47, the 12 UR is both a Type 2 and Type 4. As a Type 4, the 6 is a strong link in c3 and after removing the 1s, just one 1 remains in c3.
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Dec 23, 2008 4:57 pm    Post subject: Reply with quote

keith wrote:
Coloring on <3> abcde shows that if a is <3>, e is <3>. Strong link ef on <8>. af is an M-wing with pincers <8>. Solving R4C8 and the puzzle. Laughing

Danny, is this your "monster M-wing"?

Edit: a and e are also a W-wing, strong link <8> in C8. Taking out <3> in b, also solving the puzzzle.

No, that's not my monster M-Wing. While reviewing the puzzle before posting, my solver stopped at your W-Wing elimination.

Code:
 (9=1)a - (1)b = (1)c - (1)d = (1)e - (1)ff = (1-9)g = (9)h
 +--------------------------------------------------------------+
 |  5     4    h29    | b13    28-9  8-9   | c13    6     7     |
 |  19    8     3     |  7     6     5     |  4     19    2     |
 |  12-9  6     7     |  4     239  a19    |  5     189   38    |
 |--------------------+--------------------+--------------------|
 |  2368 f12   f126   |  5     38    7     |  9    e18    4     |
 |  389   5    g19    |  136   4     189   |  7     2     368   |
 |  389   7     4     |  136   389   2     | d13    5     368   |
 |--------------------+--------------------+--------------------|
 |  26    12    126   |  9     7     3     |  8     4     5     |
 |  7     9     8     |  2     5     4     |  6     3     1     |
 |  4     3     5     |  8     1     6     |  2     7     9     |
 +--------------------------------------------------------------+
Back to top
View user's profile Send private message
Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Dec 23, 2008 6:53 pm    Post subject: Reply with quote

Marty R. wrote:
In boxes 47, the 12 UR is both a Type 2 and Type 4.

I'm afraid the 12UR is of no help. It would be a Type 2 if the <6>s were not conjugate (in which case the Type 2 would eliminate other <6>s in c3). It would be a Type 4 if either the <1>s or the <2>s in r47c3 were conjugate (in which case whichever of the two was NOT conjugate would be eliminated from those cells). The conjugate <6>s actually destroy the 12UR.

It happens that r5c3 must be <1> due to the 6-cell 126 DP I mentioned previously. I can't see any way to get to that with just a UR.
Back to top
View user's profile Send private message Visit poster's website
Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Tue Dec 23, 2008 10:26 pm    Post subject: Reply with quote

Asellus wrote:
Marty R. wrote:
In boxes 47, the 12 UR is both a Type 2 and Type 4.

I'm afraid the 12UR is of no help. It would be a Type 2 if the <6>s were not conjugate (in which case the Type 2 would eliminate other <6>s in c3). It would be a Type 4 if either the <1>s or the <2>s in r47c3 were conjugate (in which case whichever of the two was NOT conjugate would be eliminated from those cells). The conjugate <6>s actually destroy the 12UR.

It happens that r5c3 must be <1> due to the 6-cell 126 DP I mentioned previously. I can't see any way to get to that with just a UR.

I'm sure you're right even though I don't follow the explanation. It just looks to an amateur like me that if one of the cells has to be = 6, then a 1 can't be present as a candidate in either.
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Dec 23, 2008 11:42 pm    Post subject: Reply with quote

Marty R. wrote:
It just looks to an amateur like me that if one of the cells has to be = 6, then a 1 can't be present as a candidate in either.

Marty: My turn to try and clear it up for you.

You are correct that one of [r4c3]=6 or [r7c3]=6 must be true. However, this still leaves [r7c3]=12 or [r4c3]=12, respectively. With only this information, we can not say for certain that <1> or <2> has been eliminated from both cells. The best we can say is that we could eliminate other <6s> in [c3] if they existed.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Wed Dec 24, 2008 12:09 am    Post subject: Reply with quote

Marty,

What can you say about this UR?

1. One of R47C3 is <6>. True, but not useful. There are no other candidates <6> that see both of R47C3.

2. The solutions for R47C3 are <12> and <6>. Let's try them:

Code:
+----------------+----------------+----------------+
| 5    4    29   | 13   289  89   | 13   6    7    |
| 19   8    3    | 7    6    5    | 4    19   2    |
| 129  6    7    | 4    239  19   | 5    189  38   |
+----------------+----------------+----------------+
| 2368 12   6    | 5    38   7    | 9    18   4    |
| 389  5    19   | 136  4    189  | 7    2    368  |
| 389  7    4    | 136  389  2    | 13   5    368  |
+----------------+----------------+----------------+
| 26   12   12   | 9    7    3    | 8    4    5    |
| 7    9    8    | 2    5    4    | 6    3    1    |
| 4    3    5    | 8    1    6    | 2    7    9    |
+----------------+----------------+----------------+

OR

+----------------+----------------+----------------+
| 5    4    29   | 13   289  89   | 13   6    7    |
| 19   8    3    | 7    6    5    | 4    19   2    |
| 129  6    7    | 4    239  19   | 5    189  38   |
+----------------+----------------+----------------+
| 2368 12   12   | 5    38   7    | 9    18   4    |
| 389  5    19   | 136  4    189  | 7    2    368  |
| 389  7    4    | 136  389  2    | 13   5    368  |
+----------------+----------------+----------------+
| 26   12   6    | 9    7    3    | 8    4    5    |
| 7    9    8    | 2    5    4    | 6    3    1    |
| 4    3    5    | 8    1    6    | 2    7    9    |
+----------------+----------------+----------------+


The candidate lists are valid, and both avoid the DP.

If you play them both out, you will find that one is incorrect, but you cannot decide that here and now.

Keith
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Wed Dec 24, 2008 1:21 am    Post subject: Reply with quote

I know that the more I ask, the deeper the hole I'll dig for myself. Just one question: is it a generality that a UR with a Type 2 pattern can't be used as a Type 4?
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Dec 24, 2008 1:48 am    Post subject: Reply with quote

Marty R. wrote:
I know that the more I ask, the deeper the hole I'll dig for myself. Just one question: is it a generality that a UR with a Type 2 pattern can't be used as a Type 4?

I should wait for more knowledgeable members to answer your question.

What I do know is that I've seen it mentioned more than once that searching for a UR Type 4 should occur after searching for other Types.

I know for a fact that many UR solvers search for all URs and eliminations before performing any eliminations. I recall a puzzle that had two overlapping URs. Performing only one of the URs left a difficult solution. Performing both URs as one step resulted in a reasonable solution.

What you need to remember is that a UR Type 4 also requires that one of the DP candidates be locked in an X-Wing pattern using these four cells. That's not the case above for either <1> or <2>.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Wed Dec 24, 2008 4:12 am    Post subject: Reply with quote

Marty,

I believe you can make both Type 2 and/or Type 4 eliminations on the same UR. Take a look at this:

http://www.brainbashers.com/sudokuuniquerectangles.asp

Danny is correct, that since the Type 4 takes out one of the DP candidates, it might obscure a Type 2 (or 3?).

Danny is not quite correct, in that a Type 4 only requires that one of the DP candidates be locked in the two cells with extra candidates.

A UR on an X-wing is a Type 6.

(I hope this doesn't further confuse the issue.)

Keith
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Dec 24, 2008 4:54 am    Post subject: Reply with quote

daj95376 wrote:
What you need to remember is that a UR Type 4 also requires that one of the DP candidates be locked in an X-Wing pattern using these four cells.

Example from Sudopedia:

Code:
 <27> UR Type 4 in [r79c58]  =>  [r9c58]<>2
 +-----------------------------------------------------------+
 |  2     6     8    |  4     3     7    |  1     9     5    |
 |  4     15    19   |  29    6     58   |  7     3     28   |
 |  59    3     7    |  29    1     58   |  6     28    4    |
 |-------------------+-------------------+-------------------|
 |  1     458   34   |  37    9     2    |  358   6     78   |
 |  59    25    6    |  37    8     4    |  235   1     279  |
 |  7     28    239  |  1     5     6    |  238   4     289  |
 |-------------------+-------------------+-------------------|
 |  8     9     5    |  6    *27    1    |  4    *27    3    |
 |  6     7     24   |  8     24    3    |  9     5     1    |
 |  3     124   124  |  5    *27+4  9    |  28   *27+8  6    |
 +-----------------------------------------------------------+

Code:
 X-Wing r79\c58 pattern on <7> in UR cells
 +-----------------------------------+
 |  .  .  .  |  .  .  7  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  7  .  .  |
 |  .  .  7  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  7  .  .  |  .  .  7  |
 |  .  .  .  |  7  .  .  |  .  .  7  |
 |  7  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  /  /  /  |  /  7  /  |  /  7  /  |
 |  .  7  .  |  .  .  .  |  .  .  .  |
 |  /  /  /  |  /  7  /  |  /  7  /  |
 +-----------------------------------+

keith wrote:
Danny is not quite correct, ...


keith: Do you have an example of a UR Type 4 w/o this X-Wing pattern?
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Wed Dec 24, 2008 4:58 am    Post subject: Reply with quote

I did look at that BB UR of 35-35-356-356 and it doesn't look that different from the one being discussed here, except for the other candidates present in the box. Regardless, if I came across the UR here of 12-12-126-126, I'd never recognize it as an invalid Type 4 and would make the same mistake 100 out of 100 times.
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Dec 24, 2008 5:32 am    Post subject: Reply with quote

Marty R. wrote:
Regardless, if I came across the UR here of 12-12-126-126, I'd never recognize it as an invalid Type 4 and would make the same mistake 100 out of 100 times.

Code:
 after basics: check [r47c23] for possible UR Type 4
 +--------------------------------------------------------------------+
 |  5      4     #29    |  13     289    89    |  13     6      7     |
 |  19     8      3     |  7      6      5     |  4      19     2     |
 |  129    6      7     |  4      239    19    |  5      189    38    |
 |----------------------+----------------------+----------------------|
 |  2368  *12    *126   |  5      38     7     |  9      18     4     |
 |  389    5     #19    |  136    4      189   |  7      2      368   |
 |  389    7      4     |  136    389    2     |  13     5      368   |
 |----------------------+----------------------+----------------------|
 |  26    *12    *126   |  9      7      3     |  8      4      5     |
 |  7      9      8     |  2      5      4     |  6      3      1     |
 |  4      3      5     |  8      1      6     |  2      7      9     |
 +--------------------------------------------------------------------+

Code:
 can not form X-Wing c23\r47 because [r5c3] contains <1>
 +-----------------------------------+
 |  .  /  /  |  1  .  .  |  1  .  .  |
 |  1  /  /  |  .  .  .  |  .  1  .  |
 |  1  /  /  |  .  .  1  |  .  1  .  |
 |-----------+-----------+-----------|
 |  .  1  1  |  .  .  .  |  .  1  .  |
 |  .  / #1  |  1  .  1  |  .  .  .  |
 |  .  /  /  |  1  .  .  |  1  .  .  |
 |-----------+-----------+-----------|
 |  .  1  1  |  .  .  .  |  .  .  .  |
 |  .  /  /  |  .  .  .  |  .  .  1  |
 |  .  /  /  |  .  1  .  |  .  .  .  |
 +-----------------------------------+

Code:
 can not form X-Wing c23\r47 because [r1c3] contains <2>
 +-----------------------------------+
 |  .  / #2  |  .  2  .  |  .  .  .  |
 |  .  /  /  |  .  .  .  |  .  .  2  |
 |  2  /  /  |  .  2  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  2  2  2  |  .  .  .  |  .  .  .  |
 |  .  /  /  |  .  .  .  |  .  2  .  |
 |  .  /  /  |  .  .  2  |  .  .  .  |
 |-----------+-----------+-----------|
 |  2  2  2  |  .  .  .  |  .  .  .  |
 |  .  /  /  |  2  .  .  |  .  .  .  |
 |  .  /  /  |  .  .  .  |  2  .  .  |
 +-----------------------------------+

UR Type 4 does not exist in [r47c23] !
Back to top
View user's profile Send private message
Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Dec 24, 2008 7:04 am    Post subject: Reply with quote

Marty R. wrote:
Regardless, if I came across the UR here of 12-12-126-126, I'd never recognize it as an invalid Type 4 and would make the same mistake 100 out of 100 times.

Let me try...

The thing to remember about a Type 4 is that one of the UR digits in the "roof" cells must be conjugate; this is what allows us to remove the other UR digit from those roof cells:
Code:
The <y>s in the top row are conjugate:

xya  xyb                ya   yb
          --becomes-->
xy   xy                 xy   xy

"a" and "b" are any number of other digits.

What is throwing you off is that in the puzzle above a=b=6 and those <6>s are conjugate. That is fine, but it's not Type 4. It is only Type 4 if either the <1>s or the <2>s in the "roof" are conjugate. And, if one of them were to be conjugate, then the <6>s couldn't be (or you have a hidden pair and haven't completed basic reductions).

As for a Type 4 also being a Type 2... When the non-UR digits in the roof are the same extra single digit and one of the UR digits in the roof is conjugate, then a Type 4 is also a Type 2 and vice versa. Say the roof cells are both {xya}, where "a" is a single digit and the <y>s are conjugate. If you apply Type 4 reasoning first, you get a naked {ya} pair that eliminates all other <a>s in that row or column. If you apply Type 2 reasoning first, you eliminate all the other <a>s in that row or column and now have a hidden {ya} pair. That's the difference: hidden or naked.
Back to top
View user's profile Send private message Visit poster's website
storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Dec 24, 2008 7:34 am    Post subject: Reply with quote

how about this one guys?
Code:
.------------------.------------------.------------------.
| 5     4     29   |-13    289   89   |*13    6     7    |
| 19    8     3    | 7     6     5    | 4     19    2    |
| 129   6     7    | 4     239   19   | 5     189  *38   |
:------------------+------------------+------------------:
| 2368  12    126  | 5     38    7    | 9     18    4    |
| 389   5     19   |U136   4     189  | 7     2    U368  |
| 389   7     4    |U136   389   2    | 13    5    U368  |
:------------------+------------------+------------------:
| 26    12    126  | 9     7     3    | 8     4     5    |
| 7     9     8    | 2     5     4    | 6     3     1    |
| 4     3     5    | 8     1     6    | 2     7     9    |
'------------------'------------------'------------------'

the UR on (3,6) says...
(1)r56c4 = (8)r56c9...

in other words... if r56c4 is NOT 1's then r56c9 has to be 8's

now you can form this chain

36URr56c49[(1)r56c4 = (8)r56c9] - (8=3)r3c9 - (3=1)r1c7; r1c4 <> 1

and if you look really closely at that chain why by golly gee, its a xy-wing {1,3,8}
{1=8} - (8=3) - (3=1)
Laughing Laughing Laughing
Back to top
View user's profile Send private message
Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Dec 24, 2008 9:20 am    Post subject: Reply with quote

Quote:
how about this one guys?

Well, if you note that the <6>s are an X-Wing, then external <3>s destroy the DP. This means that the UR creates the following strong inference directly:
36UR[(3)r1c4=(3)r3c9]
Thus, r1c7|r3c5<>3.

You can see that as an XY-Wing also (using your UR[1=8]). However, the logic holds even if those <3>s aren't in bivalue cells that happen to match the strong inference digits of the UR. It is also possible to see this as akin to a Skyscraper if you need to take the inferences through the UR explicitly:
(3)r1c4=36UR[(3)r56c4-(3)r56c9]=(3)r3c9
The grouped <3>s within the UR have a weak inference due to the X-Wing <6>s (if a <3> is true in both columns of the UR, then the DP results).

Once you start understanding inferences, the whole sudoku ballgame changes!
Back to top
View user's profile Send private message Visit poster's website
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Puzzles by daj All times are GMT
Goto page 1, 2  Next
Page 1 of 2

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group