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May 29th very hard puzzle
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DanPMK



Joined: 29 May 2006
Posts: 2

PostPosted: Mon May 29, 2006 9:28 pm    Post subject: May 29th very hard puzzle Reply with quote

Ok, I'm semi-new 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:
x3x|xx7|26x
xxx|x5x|x37
2xx|xxx|xxx
---+---+---
41x|xx9|3xx
36x|174|x52
xx2|8xx|xx1
---+---+---
xx3|7xx|xx9
72x|x8x|xx3
x41|3xx|72x


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

PostPosted: Mon May 29, 2006 9:39 pm    Post subject: X-Wing on the "8"s Reply with quote

Hi, DanPMK! Welcome to the forum.

The short answer is that there's an X-Wing 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

PostPosted: Mon May 29, 2006 9:42 pm    Post subject: Reply with quote

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: 5165
Location: Rochester, NY, USA

PostPosted: Tue May 30, 2006 1:07 am    Post subject: Reply with quote

After the basic stuff to eliminate candidates, I used that X-Wing 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 ab-ab-abc-abd 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 paper-and-pencil 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

PostPosted: Tue May 30, 2006 11:39 am    Post subject: Second X-Wing Reply with quote

You're right, Marty -- this is probably the toughest DailySudoku puzzle yet.

After following up on the first X-Wing (and locating a "4" at r2c3) a second X-Wing 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

PostPosted: Wed May 31, 2006 9:27 am    Post subject: May 29th Reply with quote

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

PostPosted: Wed May 31, 2006 1:50 pm    Post subject: May 29 very hard Reply with quote

I arrived at the same method like David's. It's the first time I have to use X-wing twice. Spotting x-wing 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: 5165
Location: Rochester, NY, USA

PostPosted: Wed May 31, 2006 3:46 pm    Post subject: Reply with quote

Welcome to the forum to the previous two posters. I didn't see David's second X-Wing, 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

PostPosted: Sun Jun 04, 2006 1:55 pm    Post subject: Re: X-Wing on the "8"s Reply with quote

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

PostPosted: Mon Jun 05, 2006 9:44 pm    Post subject: Another explanation of the "X-Wing" Reply with quote

Hi, riderdude! Welcome to the forum.

I'll try to explain the X-Wing logic (X-Wing 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

PostPosted: Mon Jun 05, 2006 10:11 pm    Post subject: Reply with quote

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

PostPosted: Tue Jun 06, 2006 12:16 am    Post subject: Try a "proof by contradiction" Reply with quote

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

PostPosted: Tue Jun 06, 2006 12:24 am    Post subject: Reply with quote

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



Joined: 04 Jul 2006
Posts: 5

PostPosted: Tue Jul 04, 2006 4:03 am    Post subject: Re: Second X-Wing Reply with quote

David Bryant wrote:
You're right, Marty -- this is probably the toughest DailySudoku puzzle yet.

After following up on the first X-Wing (and locating a "4" at r2c3) a second X-Wing 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 X-Wing 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:

x3x|xx7|26x
xxx|25x|x37
2xx|xxx|xxx
---+---+---
41x|529|3x6
36x|174|x52
xx2|8xx|xx1
---+---+---
xx3|7xx|xx9
72x|x8x|xx3
x41|3xx|72x
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TKiel



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

PostPosted: Tue Jul 04, 2006 12:55 pm    Post subject: Reply with quote

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

PostPosted: Tue Jul 04, 2006 6:00 pm    Post subject: Reply with quote

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

PostPosted: Tue Jul 04, 2006 10:53 pm    Post subject: Reply with quote

Laughing 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:

x3x|xx7|26x
xx4|25x|x37
2xx|xxx|xxx
---+---+---
41x|529|3x6
36x|174|x52
xx2|8xx|xx1
---+---+---
xx3|7xx|xx9
72x|x8x|xx3
x41|3xx|72x
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keith



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

PostPosted: Wed Jul 05, 2006 12:42 am    Post subject: Reply with quote

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 Type-4 Unique Rectangle eliminates <6> in R3C56.

Then, look for an X-wing 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

PostPosted: Wed Jul 05, 2006 1:03 am    Post subject: Reply with quote

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

PostPosted: Wed Jul 05, 2006 1:06 am    Post subject: Reply with quote

Geogecko,

After the single in row 7 and then the box-line interaction (exclusions in box 1), as mentioned by Keith, there is an x-wing on 8. none of which help with putting a 6 in r7c7. For that you need to spot the swordfish.

For info on terminology & techniques (although there is no consensus on terminology) you can view the following links:

www.sadmansoftware.com/sudoku/techniques.htm
www.angusj.com/sudoku/hints.php
www.scanraid.com/BasicStrategies.htm
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