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DanPMK
Joined: 29 May 2006 Posts: 2

Posted: Mon May 29, 2006 9:28 pm Post subject: May 29th very hard puzzle 


Ok, I'm seminew to this puzzle, but I think I got it down, when I run across this. I print this one out, and I get 6 numbers in. Then I get stuck. So, I look at every possible number. Still nothing definitive. So I erase and try again. I get the exact same problem. I go to the Draw/Play, and it gives me the next solution, but I think it's either some error or something I'm missing, as it doesn't seem like a logical step. Here's what I have so far:
Code:  x3xxx726x
xxxx5xx37
2xxxxxxxx
++
41xxx93xx
36x174x52
xx28xxxx1
++
xx37xxxx9
72xx8xxx3
x413xx72x

According to Draw/Play, the next step is supposed to be in row 4, column 9, and it's a number 6. This baffles me. It can be a 6, but it can also be an 8. There are other possible 6's in that row, column, and box, and I know you are never supposed to just guess in Sudoku. Am I missing something? 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Mon May 29, 2006 9:39 pm Post subject: XWing on the "8"s 


Hi, DanPMK! Welcome to the forum.
The short answer is that there's an XWing formation in rows 1 and 9 that eliminates the possibility of an "8" at r4c9. Let me explain.
 Notice the "8" at r6c4. Because of its position, we can see that the "8" in the middle left 3x3 box must lie in column 3.
 This fact, together with the "8"s in columns 4 and 5, implies that the only two places an "8" can fit in row 1 is at r1c1 or r1c9.
 We have a similar situation in row 9, where the only place for an "8" is at r9c1, or r9c9.
 So there's either an "8"at r1c1, and at r9c9. or else there's an "8" at r9c1 and at r1c9. Either way there cannot be an "8" at r4c9. dcb 

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DanPMK
Joined: 29 May 2006 Posts: 2

Posted: Mon May 29, 2006 9:42 pm Post subject: 


I see, I've never had to use the more complex logical rules when solving a puzzle. I'll have to look into them. Thanks! 

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Marty R.
Joined: 12 Feb 2006 Posts: 5162 Location: Rochester, NY, USA

Posted: Tue May 30, 2006 1:07 am Post subject: 


After the basic stuff to eliminate candidates, I used that XWing that David talked about. Later, seeing nothing else available, I tried a forcing chain from which one value resulted in a contradiction. Finally, I saw a rectangle of the abababcabd type, with the two ab's on a diagonal. I tested for c and d, and one of the values opened up the whole puzzle.
I don't know anything about Draw/Play, I'm strictly a paperandpencil guy. I found this puzzle a little more difficult than others with the same rating. 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Tue May 30, 2006 11:39 am Post subject: Second XWing 


You're right, Marty  this is probably the toughest DailySudoku puzzle yet.
After following up on the first XWing (and locating a "4" at r2c3) a second XWing emerges  on "6"s, in columns 3 & 4. I had to search pretty hard to find it. dcb 

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Huw Llewellyn
Joined: 30 May 2006 Posts: 1 Location: Canberra Australia

Posted: Wed May 31, 2006 9:27 am Post subject: May 29th 


Thanks for the tips on this one definitely the Sudoku from hell!
I have yet to see one as hard as this. Once you pointed out the second X wing I was on my way. A good one to learn advanced techniques on. 

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kkklau
Joined: 31 May 2006 Posts: 2

Posted: Wed May 31, 2006 1:50 pm Post subject: May 29 very hard 


I arrived at the same method like David's. It's the first time I have to use Xwing twice. Spotting xwing is not easy in the beginning and it is the hardest technique I can use. Beyond that I don't quite get it. 

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Marty R.
Joined: 12 Feb 2006 Posts: 5162 Location: Rochester, NY, USA

Posted: Wed May 31, 2006 3:46 pm Post subject: 


Welcome to the forum to the previous two posters. I didn't see David's second XWing, but still completed the puzzle. On just about every specific puzzle I see discussed, it is apparent that there are multiple approaches that can lead to a solution, and this, obviously, was no exception. 

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riderdude
Joined: 04 Jun 2006 Posts: 9 Location: Mass

Posted: Sun Jun 04, 2006 1:55 pm Post subject: Re: XWing on the "8"s 


David Bryant wrote:   This fact, together with the "8"s in columns 4 and 5, implies that the only two places an "8" can fit in row 1 is at r1c1 or r1c9. 
hi
new to sudoku, new to the forum.
so i start poking around to see what's what, and ran across this thread. i got everything except the statement above. why can't there be 8s in r2c1 and r7c1, based on the positions of the other 8s in columns 3, 4 and 5? 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Mon Jun 05, 2006 9:44 pm Post subject: Another explanation of the "XWing" 


Hi, riderdude! Welcome to the forum.
I'll try to explain the XWing logic (XWing on rows) one more time.
 At the position DanPMK had reached, there are only two places to fit an "8" in the first row  either at r1c1, or else at r1c9.
 There are also only two places to fit an "8" in the ninth row  either at r9c1, or else at r9c9.
 In the final solution, there has to be exactly one "8" in the first row, and there also has to be exactly one "8" in the ninth row.
 Therefore there are only two possible ways the digit "8" can fit in rows 1 and 9. Either r1c1 = 8 and r9c9 = 8, or else r1c9 = 8 and r9c1 = 8. Those are the only two ways we can fit an "8" in the first and ninth rows.
 We can conclude that the "8" in column one appears either at r1c1 or at r9c1, and that the "8" in column nine appears either at r1c9 or at r9c9. So there cannot possibly be an "8" in any other cell in these two columns. dcb 

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riderdude
Joined: 04 Jun 2006 Posts: 9 Location: Mass

Posted: Mon Jun 05, 2006 10:11 pm Post subject: 


sorry. either i'm being thick or inarticulate.
or both.
i still don't see why 8s can't go in r2c1 and r7c1, knowing that the 8 in column 3 goes either in r4c3 or r5c3, and the positions of the other 2 8s. i get everything except that. 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Tue Jun 06, 2006 12:16 am Post subject: Try a "proof by contradiction" 


riderdude wrote:  I still don't see why 8s can't go in r2c1 and r7c1, ... 
OK, maybe it will be easier to see if we use a "proof by contradiction."
 Suppose that r2c1 = 8. Then r1c1 = 8 is impossible, and we must have r1c9 = 8. But now there isn't any possible way to place an "8" in row 9  r9c1 is blocked by r2c1, and r9c9 is blocked by r1c9.
 The same logic works if we set r7c1 = 8. Again we must have r1c9 = 8, and there's still no possible way to place an "8" in row 9.
 You can turn the argument around, if you like. If r2c1 = 8 then r9c1 = 8 is impossible, and we must have r9c9 = 8. But now there isn't any possible way to place an "8" in row 1  r1c1 is blocked by r2c1, and r1c9 is blocked by r9c9.
I'm not sure how else to explain it. Anyone else care to give it a try? dcb 

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riderdude
Joined: 04 Jun 2006 Posts: 9 Location: Mass

Posted: Tue Jun 06, 2006 12:24 am Post subject: 


oh, ok. being thick.
got it.
thanks, and sorry. 

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geogecko
Joined: 04 Jul 2006 Posts: 5

Posted: Tue Jul 04, 2006 4:03 am Post subject: Re: Second XWing 


David Bryant wrote:  You're right, Marty  this is probably the toughest DailySudoku puzzle yet.
After following up on the first XWing (and locating a "4" at r2c3) a second XWing emerges  on "6"s, in columns 3 & 4. I had to search pretty hard to find it. dcb 
First post.
May I ask, how did you locate the "4" you are talking about here? I don't see a possible solution, at least, from the techniques I know, plus the XWing one I learned here.
From my current puzzle, I show that being a "469". That is the next hint given (that the "469" is a "4"), but I do not see it, am I blind or something?
In case you forgot, here is what I have so far.
Code: 
x3xxx726x
xxx25xx37
2xxxxxxxx
++
41x5293x6
36x174x52
xx28xxxx1
++
xx37xxxx9
72xx8xxx3
x413xx72x



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TKiel
Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

Posted: Tue Jul 04, 2006 12:55 pm Post subject: 


Geogecko,
With the grid as you posted it, the only places for a 4 in c9 are both in box 3 (r13c9) which means all other 4's in that box can be excluded (r3c78, r2c7). This leaves r2c3 as the only place in that row for a 4. 

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geogecko
Joined: 04 Jul 2006 Posts: 5

Posted: Tue Jul 04, 2006 6:00 pm Post subject: 


Ah, I see that now. Thanks for the tip. Sometimes those are hard to find too. I like the pattern finds better, but then that's what makes them easy. 

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geogecko
Joined: 04 Jul 2006 Posts: 5

Posted: Tue Jul 04, 2006 10:53 pm Post subject: 


This one has been the hardest one I've done so far...
So, after the 4, anyone got any logic for getting the "6" in R7C7? I have a "14568" for a possibility in that cell.
Code: 
x3xxx726x
xx425xx37
2xxxxxxxx
++
41x5293x6
36x174x52
xx28xxxx1
++
xx37xxxx9
72xx8xxx3
x413xx72x



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keith
Joined: 19 Sep 2005 Posts: 3174 Location: near Detroit, Michigan, USA

Posted: Wed Jul 05, 2006 12:42 am Post subject: 


geogecko,
In the position you posted:
Code: 
++++
 1589 3 589  49 149 7  2 6 458 
 1689 89 4  2 5 168  189 3 7 
 2 5789 56789  469 13469 1368  14589 1489 458 
++++
 4 1 78  5 2 9  3 78 6 
 3 6 89  1 7 4  89 5 2 
 59 579 2  8 36 36  49 479 1 
++++
 568 58 3  7 146 1256  14568 148 9 
 7 2 569  469 8 156  1456 14 3 
 5689 4 1  3 69 56  7 2 58 
++++ 
Look for a <2> in R7.
Then, after some line / block interactions, a Type4 Unique Rectangle eliminates <6> in R3C56.
Then, look for an Xwing on <6>.
I do not see any reductions in R7C7 at this point.
Keith 

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geogecko
Joined: 04 Jul 2006 Posts: 5

Posted: Wed Jul 05, 2006 1:03 am Post subject: 


Do you know of a web site that explains some of the techniques you are talking about?
Thanks for the assistance!
Ah, I found your post about Unique Rectangles. Thanks!
Last edited by geogecko on Wed Jul 05, 2006 1:11 am; edited 1 time in total 

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TKiel
Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI


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