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Dec 20 VH

 
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hughwill



Joined: 05 Apr 2010
Posts: 424
Location: Birmingham UK
PostPosted: Sun Dec 20, 2015 10:32 am    Post subject: Dec 20 VH Reply with quote
At last!
After basics:
Code:

+--------------+---------+-------------+
| 6    1   47  | 3  2 79 | 48  789 5   |
| 3    79  2   | 4  8 5  | 1   79  6   |
| 49   5   8   | 6  1 79 | 234 379 27  |
+--------------+---------+-------------+
| 148  48  9   | 5  7 3  | 6   2   18  |
| 158  6   15  | 9  4 2  | 38  378 178 |
| 7    2   3   | 8  6 1  | 5   4   9   |
+--------------+---------+-------------+
| 1489 489 14  | 12 3 6  | 7   5   28  |
| 158  78  157 | 12 9 4  | 28  6   3   |
| 2    3   6   | 7  5 8  | 9   1   4   |
+--------------+---------+-------------+

Play this puzzle online at the Daily Sudoku site

Looks like it needs two XY-wings to me:
Quote:
49-7 pivot r1c3 (or 47-9 pivot r1c3) followed by 79-4 pivot r2c2
Unless anyone knows different....

Hugh
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Dec 20, 2015 4:11 pm    Post subject: Reply with quote
I agree.
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dongrave



Joined: 06 Mar 2014
Posts: 568
PostPosted: Sun Dec 20, 2015 5:00 pm    Post subject: Reply with quote
I had the same as Hugh too - but I'm also on a single-step chain-finding kick and this was the only one that I could find. I'm sure someone out there must have something better. (Oh, someone had better check this for accuracy too. I'm still sort of new at these.)

(7=9)r2c2-(9=4)r3c1-r4c1=r4c2-(49=8)r7c2-(8=2)r7c9-(2=7)r3c9-(7=9)r3c6-(9=7)r1c6 => r1c3<>7 which solves it (I think).
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Dec 20, 2015 5:39 pm    Post subject: Reply with quote
dongrave wrote:
I had the same as Hugh too - but I'm also on a single-step chain-finding kick and this was the only one that I could find. I'm sure someone out there must have something better. (Oh, someone had better check this for accuracy too. I'm still sort of new at these.)

(7=9)r2c2-(9=4)r3c1-r4c1=r4c2-(49=8)r7c2-(8=2)r7c9-(2=7)r3c9-(7=9)r3c6-(9=7)r1c6 => r1c3<>7 which solves it (I think).


The chain looks legitimate to me. However, your deletion effectively does the same as the 47-9 XY-Wing, but that wasn't enough to solve.
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dongrave



Joined: 06 Mar 2014
Posts: 568
PostPosted: Sun Dec 20, 2015 6:05 pm    Post subject: Reply with quote
Marty R. wrote:

The chain looks legitimate to me. However, your deletion effectively does the same as the 47-9 XY-Wing, but that wasn't enough to solve.

No, that can't be right Marty. The XY wing gave us r13c6; my chain gives us r1c3=4 which solves it. (I always make sure that a chain solves the puzzle so I know it's a one-stepper.) Thanks!
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Sun Dec 20, 2015 6:50 pm    Post subject: Reply with quote
dongrave wrote:
(7=9)r2c2-(9=4)r3c1-r4c1=r4c2-(49=8)r7c2-(8=2)r7c9-(2=7)r3c9-(7=9)r3c6-(9=7)r1c6 => r1c3<>7 which solves it (I think).
A shorter chain :
Code:
+-------------------+-------------+----------------+
| 6     1      (47) | 3   2  9(7) | 48   789  5    |
| 3     (79)   2    | 4   8  5    | 1    79   6    |
| 49    5      8    | 6   1  9(7) | 234  379  (27) |
+-------------------+-------------+----------------+
| 148   48     9    | 5   7  3    | 6    2    18   |
| 158   6      15   | 9   4  2    | 38   378  178  |
| 7     2      3    | 8   6  1    | 5    4    9    |
+-------------------+-------------+----------------+
| 1489  (489)  1-4  | 12  3  6    | 7    5    (28) |
| 158   78     157  | 12  9  4    | 28   6    3    |
| 2     3      6    | 7   5  8    | 9    1    4    |
+-------------------+-------------+----------------+
[XY-Wing(-479)L1C3,L27C2=8L7C2-(8=27)L73C9-7L3C3=7L1C6-(7=4)L1C3]-(4=1)L7C3
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Dec 20, 2015 7:00 pm    Post subject: Reply with quote
Code:
+--------------+---------+-------------+
| 6    1   47  | 3  2 79 | 48  789 5   |
| 3    79  2   | 4  8 5  | 1   79  6   |
| 49   5   8   | 6  1 79 | 234 379 27  |
+--------------+---------+-------------+
| 148  48  9   | 5  7 3  | 6   2   18  |
| 158  6   15  | 9  4 2  | 38  378 178 |
| 7    2   3   | 8  6 1  | 5   4   9   |
+--------------+---------+-------------+
| 1489 489 14  | 12 3 6  | 7   5   28  |
| 158  78  157 | 12 9 4  | 28  6   3   |
| 2    3   6   | 7  5 8  | 9   1   4   |
+--------------+---------+-------------+


Don, you're gonna have to show me what I'm doing wrong.

Your chain => r1c3<>7=4
(7=4)r1c3-(4=9)r3c1-(9=7)r3c6. Here we are, doing the same thing as the 47-9 XY-Wing, removing 9 from r3c6, leaving a 7 there. That wasn't enough to solve and we had to go to a second wing.
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dongrave



Joined: 06 Mar 2014
Posts: 568
PostPosted: Sun Dec 20, 2015 8:17 pm    Post subject: Reply with quote
Marty R. wrote:

Don, you're gonna have to show me what I'm doing wrong.

Your chain => r1c3<>7=4
(7=4)r1c3-(4=9)r3c1-(9=7)r3c6. Here we are, doing the same thing as the 47-9 XY-Wing, removing 9 from r3c6, leaving a 7 there. That wasn't enough to solve and we had to go to a second wing.


Hi Marty, The difference is that the XY wing does not solve box 1 whereas the chain does - so the 4 in r1c3 gives us r1c7<>4=8 and r7c3<>4=1 and then they just branch out everywhere and solve the puzzle. It's an easy thing to overlook so I should have mentioned it in my previous post!
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Dec 20, 2015 10:14 pm    Post subject: Reply with quote
OK, I had a similar situation here:

Code:
+----------+-------------+--------+
| 19 2  19 | 6    3   7  | 8  4 5 |
| 37 67 36 | 45   45  8  | 9  1 2 |
| 8  5  4  | 2    1   9  | 3  6 7 |
+----------+-------------+--------+
| 2  67 39 | 3479 479 1  | 46 5 8 |
| 39 4  5  | 8    69  36 | 2  7 1 |
| 17 8  16 | 47   2   5  | 46 3 9 |
+----------+-------------+--------+
| 5  9  2  | 37   67  36 | 1  8 4 |
| 6  1  8  | 59   59  4  | 7  2 3 |
| 4  3  7  | 1    8   2  | 5  9 6 |
+----------+-------------+--------+


I knew the correct solution in advance. My original answer had r4c5=4, which I knew to be correct. However when starting out solving that cell, it wouldn't complete. So I reworked my chains and was able to force r7c5=7, which goes all the way when solving that cell first.
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