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Korky
Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK
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 Posted: Wed Jul 11, 2007 10:36 am Post subject: Graded "Too Hard" by Daily Sudoku |
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Can anyone give me a clue? All I can see is that R2C1 can't reduce to 89 (deadly pattern) so must contain either a 3 or 4
| Code: |
+--------------+----------+----------+
| 1 2 5 | 8 9 7 | 6 3 4 |
| 3489 3489 89 | 5 234 6 | 12 129 7 |
| 6 349 7 | 1 234 34 | 5 29 8 |
+--------------+----------+----------+
| 48 478 2 | 6 1 45 | 9 57 3 |
| 5 34 6 | 7 34 9 | 18 18 2 |
| 39 379 1 | 2 8 35 | 4 57 6 |
+--------------+----------+----------+
| 2 1 4 | 9 7 8 | 3 6 5 |
| 7 5 3 | 4 6 1 | 28 28 9 |
| 89 6 89 | 3 5 2 | 7 4 1 |
+--------------+----------+----------+
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Play this puzzle online at the Daily Sudoku site |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jul 11, 2007 11:06 am Post subject: |
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Right, so take out <89> from R2C1.
Then, you will find two finned X-wings on <3>, and a finned X-wing on <4> that solve it. All of the eliminations are in boxes 1 and 2.
I suspect the UR reduction is not needed, and after one or two of the finned X-wings, there is an XY-wing I did not use.
Keith |
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Korky
Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK
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| Posted: Wed Jul 11, 2007 11:11 am Post subject: |
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| Thanks Keith. I'm working on it. |
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Korky
Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK
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| Posted: Wed Jul 11, 2007 12:04 pm Post subject: |
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Keith, following your clues, one finned x-wing on 3 and another on 4 eliminated both from R2C5 and the puzzle collapsed.
Thanks again! |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Wed Jul 11, 2007 12:19 pm Post subject: |
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If you are prepared to assume that the puzzle has a unique solution, there is a quicker way.
9 may be placed in r2c8 using the unique six r258c78.
Steve |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Wed Jul 11, 2007 12:33 pm Post subject: |
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A uniqueness triple - first time I've seen that.
Similar to the finned x-wings but maybe easier to spot because they're simple strong links:
Eliminates 3&4 from r3c2. |
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Korky
Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK
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| Posted: Wed Jul 11, 2007 2:19 pm Post subject: |
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| I think the unique six is very neat. I'll look for it in future. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Jul 11, 2007 4:37 pm Post subject: |
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| Steve R wrote: | If you are prepared to assume that the puzzle has a unique solution, there is a quicker way.
9 may be placed in r2c8 using the unique six r258c78.
Steve |
Steve, could you explain the logic for those of us (i.e., me) who are too dense to see it? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jul 11, 2007 5:31 pm Post subject: |
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Marty,
This pattern:
| Code: | +----------+----------+----------+
| . . . | 12 . 12| . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . . . | 23 . 23| . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | 13 . 13| . . . |
| . . . | . . . | . . . |
+----------+----------+----------+ |
is not unique. Try it. Pick <1> in R1C4. Then pick <2>. Both lead to a solution.
The complete situation would have to be something like:
| Code: | +----------+----------+----------+
| . . . | 12 . 12| . 3 . |
| . . . | . . . | . . . |
| . . . | . 3 . | . . . |
+----------+----------+----------+
| . . . | 23 . 23| . 1 . |
| . . . | . . . | . . . |
| . . . | . 1 . | . . . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | 13 . 13| . 2 . |
| . . . | . 2 . | . . . |
+----------+----------+----------+ |
so it is indeed true you can interchange the solutions and still have a single 1,2,3 in each row, column and block.
Something I have seen before:
| Code: | +----------+----------+----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . 12 . | 12 . . | . . . |
| . . . | . . . | . . . |
| . 12 . | . . 12| . . . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | 12 . 12| . . . |
| . . . | . . . | . . . |
+----------+----------+----------+ |
Is the following possible? I don't know.
| Code: | +----------+----------+----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . 12 . | 23 . . | . . . |
| . . . | . . . | . . . |
| . 12 . | . . 23| . . . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | 13 . 13| . . . |
| . . . | . . . | . . . |
+----------+----------+----------+ |
Best wishes,
Keith |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Wed Jul 11, 2007 6:06 pm Post subject: |
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I don’t think Keith’s last pattern has any bearing on the number of solutions. As far as I know there are just three patterns of six cells. One is aligned (in two columns or rows) as in the original puzzle; one is bent (i.e. goes round a corner) as in Keith’s penultimate example. The third (skew) is even less useful than the other two:
| Code: | +----------+------------+----------+
| . . . | . . . | . . . |
| . . . | 12 12 . | . . . |
| . . . | . . . | . . . |
+----------+------------+----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . 12 12 | . . . |
+----------+------------+----------+
| . . . | . . . | . . . |
| . . . | 12 . 12 | . . . |
| . . . | . . . | . . . |
+----------+------------+----------+ |
The bent version is not restricted to six cells even in a 9 x 9 grid. If he had wished, and started in the first box rather than the fourth, Keith could have gone round the board with it.
Regards
Steve |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Jul 11, 2007 9:10 pm Post subject: |
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| Thanks guys. |
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jLo
Joined: 30 Apr 2007
Posts: 55
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| Posted: Thu Jul 12, 2007 5:19 am Post subject: |
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| What about using the W-wing right from the beginning? |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Thu Jul 12, 2007 11:10 pm Post subject: |
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Coloring on <3>and coloring on <4> leaves 9 as the only possibility in r3c2.
It occurred to me after I posted that my coloring on 3 & 4 was the same as jLo's W-wing and it turns out that it was. Also turns out the (3,4) pairs in r3c6 & r5c2 are connected by strong links on both 3 and 4. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Fri Jul 13, 2007 7:38 am Post subject: |
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| keith wrote: |
Is the following possible? I don't know.
| Code: | +----------+----------+----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . 12 . | 23 . . | . . . |
| . . . | . . . | . . . |
| . 12 . | . . 23| . . . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | 13 . 13| . . . |
| . . . | . . . | . . . |
+----------+----------+----------+ |
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Yes, the 2's or 3's in boxes 2, 4, 6 or 8 could "fix" it to one solution. This is deadly:
| Code: | +----------+----------+----------+
| . . . | 12 . 12| . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . 12 . | 23 . . | . 13 . |
| . . . | . . . | . . . |
| . 12 . | . . 23| . 13 . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | 13 . 13| . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
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