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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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 Posted: Mon May 05, 2008 4:17 am Post subject: MOTT |
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M6124110 (45)
| Code: |
+-------------+-----------------+-------------+
| 7 236 4 | 136 5 26 | 9 123 8 |
| 36 23569 25 | 13689 2379 2678 | 24 12347 17 |
| 8 239 1 | 39 2379 4 | 6 237 5 |
+-------------+-----------------+-------------+
| 1 578 57 | 4 68 9 | 28 2568 3 |
| 9 58 6 | 2 1 3 | 7 58 4 |
| 2 4 3 | 7 68 5 | 1 68 9 |
+-------------+-----------------+-------------+
| 4 237 9 | 38 237 1 | 5 78 6 |
| 36 12367 27 | 5 2379 2678 | 48 14789 17 |
| 5 167 8 | 69 4 67 | 3 179 2 |
+-------------+-----------------+-------------+
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Play this puzzle online
There's a nice mix of techniques here in this middle-o-t-road puzzle, starting with a type 1. (Mostly -wings of various kinds for me.) |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon May 05, 2008 4:44 am Post subject: |
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the {6,8} UR sticks out at first glance.
I xy-chain sawed it to death.  |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon May 05, 2008 7:02 am Post subject: |
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After the UR,
kite on 2:-r2c3=r8c3-r7c2=r7c5- ,
kite on 7:-r8c9=r2c9-r3c8=r3c5- ,
and ...
edit: ********* ERRONEOUS GRID and conclusions removed *********
Last edited by nataraj on Mon May 05, 2008 11:45 am; edited 1 time in total |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Mon May 05, 2008 9:30 am Post subject: |
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| Quote: | | Middle-of-the-road? |
I suppose I meant standard named techniques only. I agree that quite a few are needed. Mostly though, it's down to luck: you must have used a different DP from the one that Norm & I used. If you start with the 68 UR you get:
| Code: | +-------------+-----------------+-------------+
| 7 236 4 | 136 5 26 | 9 123 8 |
| 36 23569 25 | 13689 2379 2678 | 24 12347 17 |
| 8 239 1 | 39 2379 4 | 6 237 5 |
+-------------+-----------------+-------------+
| 1 578 57 | 4 6 9 | 28 25 3 |
| 9 58 6 | 2 1 3 | 7 58 4 |
| 2 4 3 | 7 8 5 | 1 6 9 |
+-------------+-----------------+-------------+
| 4 237 9 | 38 237 1 | 5 78 6 |
| 36 12367 27 | 5 2379 2678 | 48 14789 17 |
| 5 167 8 | 69 4 67 | 3 179 2 |
+-------------+-----------------+-------------+ |
And that has a 25 W-wing (in r2 & r4) to help things along. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon May 05, 2008 10:34 am Post subject: |
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Thank you, Victor - I used the same 68 DP but I made a stupid mistake.
Instead of removing 6 and 8 from r4c8, giving 25 I somehow wrote 28 and worked from there. As it happens (because r4c8=2), that wrong "assumption" still yielded a valid solution, otherwise I might have realized the error myself.
All my posted grids inherit the initial mistake.
I'll start again. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon May 05, 2008 11:40 am Post subject: |
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Ah... this looks much different now.
I still used the kites. After the w-wing (25, linked by col 7) the road is rather smooth and I arrive at two xy-wings (36-39-69 and 37-38-78 in boxes 7 and 8 ), and finally here:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 7 236 4 | 16 5 26 | 9 123 8 |
| 36 2369 5 | 168 379 268 | 24 12347 17 |
| 8 239 1 | 39 379 4 | 6 237 5 |
+--------------------------+--------------------------+--------------------------+
| 1 58 7 | 4 6 9 | 28 25 3 |
| 9 58 6 | 2 1 3 | 7 58 4 |
| 2 4 3 | 7 8 5 | 1 6 9 |
+--------------------------+--------------------------+--------------------------+
| 4 37 9 | 38 2 1 | 5 78 6 |
| 36 136 2 | 5 39 78 | 48 14789 17 |
| 5 17 8 | 69 4 67 | 3 179 2 |
+--------------------------+--------------------------+--------------------------+
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A w-wing (17 in r8c9 and r9c2, connected this time by row 7) kills 1 in r8c2 (and r9c8) and solves the puzzle.
All in all, one UR, two w-wings, two xy-wings (and two - possibly optional - kites) ... quite a nice showcase for advanced solving methods. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon May 05, 2008 3:37 pm Post subject: |
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I am exhausted! 
I thought that this puzzle was over several times only to have to find another advanced technique to make further progress. I seemed to find the same set of techniques already mentioned including the UR, w-wings and xy-wings, but I started off with a finned x-wing on 2 plus multi-coloring on 7, both of which did not seem to provide any real help.
Ted |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon May 05, 2008 3:37 pm Post subject: |
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Almost one-step solution:
I kept thinking about the UR mix-up all afternoon.
Finally I went back to the original grid. There are actually TWO URs:
a) Type 1 68 r46c58, removes 6 and 8 from r4c8 (and it destroys the other UR!)
b) Type ? 58 r45c28 with strong link on 5 in col 8 removes 8 from r4c2 (and it destroys the other UR!)
But if we know we can remove 6,8 from r4c8 and that we can remove 8 from r4c2, why not remove them at the same time?
The resulting grid has all singles almost to the end:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 7 36 4 | 16 5 2 | 9 13 8 |
| 36 9 5 | 168 37 68 | 2 4 17 |
| 8 2 1 | 39 379 4 | 6 37 5 |
+--------------------------+--------------------------+--------------------------+
| 1 5 7 | 4 6 9 | 8 2 3 |
| 9 8 6 | 2 1 3 | 7 5 4 |
| 2 4 3 | 7 8 5 | 1 6 9 |
+--------------------------+--------------------------+--------------------------+
| 4 37 9 | 38 2 1 | 5 78 6 |
| 36 1367 2 | 5 39 678 | 4 1789 17 |
| 5 167 8 | 69 4 67 | 3 179 2 |
+--------------------------+--------------------------+--------------------------+
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A single xy-wing 37-78-38 removes 3 from r3c4 and solves the puzzle.
I did read in one of the UR reference posts (I think it was keith's, not sure) that some UR eliminations destroy other URs. This is the first time I actually saw this in action...
Lesson learnt: if there is more than one UR type elimination possible in a grid, don't do them in sequence but in parallel.   |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Mon May 05, 2008 8:58 pm Post subject: |
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| Quote: | | Lesson learnt: if there is more than one UR type elimination possible in a grid, don't do them in sequence but in parallel. |
Nice idea. Definitely OK, is it, I mean to do two URs simultaneously?
Sorry, Ted! If it's any comfort, which it probably isn't, it took me quite some time to do as well.
(PS. You don't need it, but there's an M-wing as well towards the end. Look at the two 78s in Nataraj's second last grid, in r78. They're connected by the 8s, and you can extend the 7 in r8c6 down to r9c6. That removes the 7 from r9c8.) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue May 06, 2008 7:09 pm Post subject: |
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| Victor wrote: | | Definitely OK, is it, I mean to do two URs simultaneously? |
Yes.
All Deadly Pattern-based eliminations that are present in a grid are valid, even if performing any of those eliminations appears to destroy one or more of the other Deadly Patterns.
Even a single DP might have two different eliminations possible. For instance, a Type 4 UR might also have a Type 3 elimination. It is easy to overlook one of these if you spot the other one first. |
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