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July 24 VH

 
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prakash



Joined: 02 Jan 2008
Posts: 67
Location: New Jersey, USA

PostPosted: Wed Jul 23, 2008 11:39 pm    Post subject: July 24 VH Reply with quote

My way involved a straight forward XY wing on 389 which eliminated the 8 in R9C7. The rest was smooth sailing.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Jul 24, 2008 12:34 am    Post subject: Reply with quote

I saw at least three solutions. Highlight inside the quote if you want to see them.

Quote:
After basics, there were at least three ways that were apparent to solve the puzzle:

1) XY-Wing on 389
2) BUG+2
3) At least one XY-Chain
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Jul 24, 2008 6:01 am    Post subject: Reply with quote

Basics really take you almost all the way...

After basics:
Code:

+--------------------------+--------------------------+--------------------------+
| 4       2       8        | 5       6       3        | 1       7       9        |
| 9       1       3        | 8       47      47       | 6       5       2        |
| 6       5       7        | 9       1       2        | 348     38      48       |
+--------------------------+--------------------------+--------------------------+
| 78      3       69       | 46      2       78       | 49      1       5        |
| 78      69      1        | 46      378     5        | 2       39      47       |
| 2       4       5        | 37      9       1        | 38      6       78       |
+--------------------------+--------------------------+--------------------------+
| 5       69      69       | 1       48      48       | 7       2       3        |
| 1       8       2        | 37      37      9        | 5       4       6        |
| 3       7       4        | 2       5       6        | 89      89      1        |
+--------------------------+--------------------------+--------------------------+


any one of these moves will do (did not look at the BUG+2 yet):
xy-wing 38-39-89 col 7 box 6

m-wing (38 r3c8 via col 7 to 78 in r6c9)
m-wing (38 r6c7 via row 3 to 89 in r9c8)
w-wing 38 (r3c8,r6c7) via row 9 or col 9

---

edit 2010 GMT+2 to remove erroneous mention of the xy-wing 78-37-38 row 6 box 5. It is in fact useless.


Last edited by nataraj on Thu Jul 24, 2008 6:10 pm; edited 1 time in total
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andras



Joined: 31 Oct 2007
Posts: 56
Location: Mid Wales

PostPosted: Thu Jul 24, 2008 6:53 am    Post subject: Reply with quote

A very nice puzzle, I thought; basics solve most of it, and I saw the xy-wing without tearing out too much of my hair or losing too much of my crossword time later!

John
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LloydB



Joined: 09 Jul 2007
Posts: 21
Location: Skagit Co., WA USA

PostPosted: Thu Jul 24, 2008 9:29 am    Post subject: Reply with quote

The 389 xy-wing solved it for me.

The 378 xy-wing in box 5 Nataraj mentioned doesn't seem to do any thing for me.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Thu Jul 24, 2008 1:47 pm    Post subject: Reply with quote

Part way through basics I felt that the puzzle would be solved by a BUG, and sure enough, the bivalues keep popping up like daffodils in the spring. However I could not solve the BUG+2 that I reached, and finally looked for another solution that readily appeared as the <389> xy-wing.

If anyone solved the BUG+2 condition, I would appreciate the details.

Ted Crying or Very sad
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Thu Jul 24, 2008 2:39 pm    Post subject: Reply with quote

The Bug+2 references are interesting because I could clearly see after basics that there were only two cells with tri-values. I'd heard of Bug+2's but after a lot of searching I could only find one explanation. This suggested that unless the two Bug+1 eliminations were stongly linked, one had to use "forcing chains" (that's how I read it anyway). I didn't see strong links here - and I see that doing two independent Bug+1s doesn't work either. (But then I guess it's not supposed to).
So my interpretation of Bug+2s is that unless the Bug+1 eliminations offer a solution by "seeing" each other - one has to guess. Right???
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
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PostPosted: Thu Jul 24, 2008 3:43 pm    Post subject: Reply with quote

As to the BUG+2, either r5c5 must be 7 or r3c7 must be 8. The former leads to an invalid solution, thus reducing it to a BUG+1.
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cgordon



Joined: 04 May 2007
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Location: ontario, canada

PostPosted: Thu Jul 24, 2008 3:52 pm    Post subject: Reply with quote

Quote:
As to the BUG+2, either r5c5 must be 7 or r3c7 must be 8. The former leads to an invalid solution, thus reducing it to a BUG+1.


Marty: I guess my question is how does it lead to an invalid solution. Seems that unless both eliminations are strongly linked, it's down to guesswork, which in itself is an invalid solution - or should be.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Jul 24, 2008 5:06 pm    Post subject: Reply with quote

cgordon wrote:
Quote:
As to the BUG+2, either r5c5 must be 7 or r3c7 must be 8. The former leads to an invalid solution, thus reducing it to a BUG+1.


Marty: I guess my question is how does it lead to an invalid solution. Seems that unless both eliminations are strongly linked, it's down to guesswork, which in itself is an invalid solution - or should be.

I did this more than once: setting r5c5 to 7 and making eliminations therefrom leads to duplicate numbers in a house.

It is guesswork in a way, and I have questioned such things in the past, not necessarily BUG+2, asking why this isn't a forcing chain, or just plain trial and error. People much better at this game than I am seem to accept it when it's discovered based on a pattern, as opposed to a chain where, for example, you test each value of a bivalue cell to see what happens.

Another example might be a UR 34-34-345-346. One of those trivalue cells must be a 5 or 6, works just like a forcing chain, but is acceptable to some because it was found via the pattern.

Hope this makes some sense.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Thu Jul 24, 2008 5:37 pm    Post subject: Reply with quote

Marty,

Thanks for the explanation. In fact, I had performed just what you indicated and found the same conclusion: that r5c5=7 resulted in an invalid puzzle, but I did not then eliminate the 7 from that cell to derive a BUG+1 situation.

I understand your logic in eliminating a candidate that creates an invalid solution and will keep it in mind for the future.

Thanks again...

Ted
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Jul 24, 2008 6:09 pm    Post subject: Reply with quote

LloydB wrote:
The 389 xy-wing solved it for me.

The 378 xy-wing in box 5 Nataraj mentioned doesn't seem to do any thing for me.


Sorry LloydB. the xy wing is indeed useless.

I'll make the correction in my post. Thanks!
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Clement



Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania

PostPosted: Thu Jul 24, 2008 6:50 pm    Post subject: Daily Sudoku: Thu 24- Jul-2008 VH Reply with quote

XY-Wing 389 Pivot {3,8}r6c7 with Pincers {3,9}r5c8 and {8,9}r9c7 eliminating 9 in r9c8 solving the puzzle.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Jul 24, 2008 8:27 pm    Post subject: Reply with quote

I think I found a way to exploit that BUG+2 without resorting to forcing chains:

The BUG+2 establishes a strong link between r5c5 and r3c7 (either r5c5=7 or r3c7=8).
That means, if r5c5 is NOT 7 then r3c7 must be 7 (and vice versa).

One way to make r5c5<>7 is if r4c6=7 which is the case if r4c7=3.

Now we have a nice elimination:
If r6c7 is not 8 then (r6c7=3,r6c4=7,r5c5<>7) then r4c7=8.
That means r9c7 cannot be 8

Written as an AIC:
-(8=3)r6c7-(3=7)r6c4-[BUG+2:(7)r5c5=(8)r4c7]- ;r9c7<>8
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Fri Jul 25, 2008 5:05 am    Post subject: Reply with quote

Or, a finned XY-wing!
Code:
+-------------+-------------+-------------+
| 4   2   8   | 5   6   3   | 1   7   9   |
| 9   1   3   | 8   47  47  | 6   5   2   |
| 6   5   7   | 9   1   2   |348a 38  48b |
+-------------+-------------+-------------+
| 78  3   69  | 46  2   78  | 49  1   5   |
| 78  69  1   | 46  378 5   | 2   39  47  |
| 2   4   5   | 37  9   1   | 38c 6   78d |
+-------------+-------------+-------------+
| 5   69  69  | 1   48  48  | 7   2   3   |
| 1   8   2   | 37  37  9   | 5   4   6   |
| 3   7   4   | 2   5   6   |-89  89  1   |
+-------------+-------------+-------------+

Look at a, b, and c. Either a is <8>, or the XY-wing bac is true: a is <34>. The XY-wing eliminates <8> in d, solving c as <8>. (Look at R6.)

Either way, the <8> in C7 cannot be in R9C7, and the puzzle is solved.

Keith Very Happy Very Happy
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Fri Jul 25, 2008 5:50 am    Post subject: Reply with quote

Thinking about that BUG+2 elimination some more, I come to view it as something very similar to what we do in multi coloring, like a kite for example.
I once called such a pattern (where there are two strong rods connected by a weak chain) a nunchuck Wink

Only this time the strong links are not in one single candidate, but in two different candidates (that is how the strong link can "jump" from r5c5 to r3c7).

Look at this drawing - I marked the strong link induced by the BUG+2 and the strong link in row 6.



Both links connect a "7" candidate in one cell with an "8" candidate in another cell. And box 5 provides the necessary (weak) link between the two strong links.

Finally, the poor "8" that sees both ends of the nunchuck gets killed
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Jul 25, 2008 11:06 am    Post subject: Reply with quote

As an alternative to the BUG+2 I think you can simply place 3 in r5c5 using the deadly pattern marked by + signs:

Code:
+-------------------------------------------+
| 4    2   8  | 5   6     3   | 1    7   9  |
| 9    1   3  | 8   47+   47+ | 6    5   2  |
| 6    5   7  | 9   1     2   | 348  38  48 |
---------------------------------------------
| 78+  3   69 | 46  2     78+ | 49   1    5 |
| 78+  69  1  | 46  78+3  5   | 2    39  47 |
| 2    4   5  | 37  9     1   | 38   6   78 |
---------------------------------------------
| 5    69  69 | 1   48+   48+ | 7    2   3  |
| 1    8   2  | 37  37    9   | 5    4   6  |
| 3    7   4  | 2   5     6   | 89   89  1  |
+-------------------------------------------+

Steve
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DennyOR



Joined: 12 Sep 2007
Posts: 33
Location: Portland, Oregon

PostPosted: Fri Jul 25, 2008 5:14 pm    Post subject: Reply with quote

The 38-84-47-78-83 xy-chain solved it for me, eliminating the 3 in r5c8.
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