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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Mon Dec 10, 2007 11:02 pm Post subject: A great finish! |
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This one has a great ending, which I found with Medusa Coloring.
| Code: | Puzzle: M5223942sh(15)
+-------+-------+-------+
| . . . | 8 . . | . . . |
| . . 5 | . . 6 | 7 . . |
| 8 . 4 | 5 9 . | 3 . 2 |
+-------+-------+-------+
| 2 . . | . 1 . | . . 9 |
| . . . | 3 . 9 | . . . |
| . 4 9 | . 2 . | 8 1 . |
+-------+-------+-------+
| 7 . 3 | 2 8 . | 5 . 6 |
| . . 2 | . . 7 | 1 . . |
| . . . | 1 . . | . . . |
+-------+-------+-------+ |
After the basics, there is a rare WXY-wing, which is of no help at all. Then what? (Hint: Contemplate what R1C2 could be.)
The candidates are sparse enough that I think there are probably a number of creative ways to end this.
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Dec 11, 2007 2:08 am Post subject: |
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| Code: | 136 36# 16# | 8 7 2 | 9 45 45
9 2 5 | 4 3 6 | 7 8 1
8 7 4 | 5 9 1 | 3 6 2
------------------------------------------------------------------------
2 35# 67 | 67 1 8 | 4 35 9
15# 58 178 | 3 4 9 | 6 2 57
36 4 9 | 67 2 5 | 8 1 37
------------------------------------------------------------------------
7 1 3 | 2 8 4 | 5 9 6
456 568 2 | 9 56 7 | 1 34 348
456 9 68 | 1 56 3 | 2 7 48
the # is an xy-chain eliminates 1 in r1c1 |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Dec 11, 2007 2:13 am Post subject: |
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| Code: | 36 36# 16 | 8 7 2 | 9 45 45
9 2 5 | 4 3 6 | 7 8 1
8 7 4 | 5 9 1 | 3 6 2
------------------------------------------------------------------------
2 35# 67# | 67 1 8 | 4 35 9
15 58# 78# | 3 4 9 | 6 2 57
36# 4 9 | 67 2 5 | 8 1 37
------------------------------------------------------------------------
7 1 3 | 2 8 4 | 5 9 6
45 68 2 | 9 56 7 | 1 34 348
45 9 68 | 1 56 3 | 2 7 48 |
anothr xy-chain starting at r6c1 ends at r1c2 takes the 6 at r1c1
that should solve it |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Dec 11, 2007 2:15 am Post subject: |
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This was harder than it looked, what with the large number of cells with just a few candidates. There was an XYZ-Wing right off the bat, then it resisted all my efforts at X, XY, XYZ, W, Skyscrapers, UR, ER and coloring.
| Quote: | | This one has a great ending, which I found with Medusa Coloring. |
Some years ago I was heavily into Greek mythology, but never came across any Sudoku tips. Medusa was slain by Perseus and Marty was slain by Medusa. But the puzzle easily succumbed to an XY-Chain. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Dec 11, 2007 5:06 am Post subject: |
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Here's what I noticed:
| Code: | +-------------+-------------+-------------+
| 136 36# 1-6 | 8 7 2 | 9 45 45 |
| 9 2 5 | 4 3 6 | 7 8 1 |
| 8 7 4 | 5 9 1 | 3 6 2 |
+-------------+-------------+-------------+
| 2 35% 67@ | 67 1 8 | 4 35 9 |
| 15 58 178 | 3 4 9 | 6 2 57 |
| 36# 4 9 | 67 2 5 | 8 1 37 |
+-------------+-------------+-------------+
| 7 1 3 | 2 8 4 | 5 9 6 |
| 45 568 2 | 9 56 7 | 1 34 348 |
| 456 9 68 | 1 56 3 | 2 7 48 |
+-------------+-------------+-------------+ |
1. The cells # have the same value, either <3> or <6>. Look at coloring on <3> via %.
2. There is a strong link on <6> in B4, connecting the cells # @ in that block. Either # or @ is <6>, R1C3 cannot be <6>.
After some cleaning up, you have a BUG+1: R8C9 must be <4>.
I've never seen this (in this way) before. It's kind of like a W-wing:
XM=Xy=XM=M where y is any candidates, and = is a strong link in X or M, as the case may be. Any cell that sees both ends cannot be M.
Very cool, I think. 
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Tue Dec 11, 2007 9:44 am Post subject: |
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| Code: | 136 36 16 | 8 7 2 | 9 45 45
9 2 5 | 4 3 6 | 7 8 1
8 7 4 | 5 9 1 | 3 6 2
------------------------------------------------------------------------
2 35 67 | 67 1 8 | 4 35 9
15 58 178 | 3 4 9 | 6 2 57
36 4 9 | 67 2 5 | 8 1 37
------------------------------------------------------------------------
7 1 3 | 2 8 4 | 5 9 6
456 568 2 | 9 56 7 | 1 34 348
456 9 68 | 1 56 3 | 2 7 48
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What i just described in the other thread, can easiliy be done here: Explore the strong link for 8 in row 8. Is there a way from 8 in r8c2 to 3 or 4 in a cell, that sees r8c9 ? (if not try to find a way from r8c9=8 to a 5 or 6, that sees r8c2)
r8c2=8 => r5c2=5 => r5c9=7 => r6c9=3
=> r8c9<>3 |
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re'born
Joined: 28 Oct 2007
Posts: 80
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| Posted: Tue Dec 11, 2007 9:54 am Post subject: |
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| Code: | .---------------.---------------.---------------.
| 136% 36 16% | 8 7 2 | 9 45 45 |
| 9 2 5 | 4 3 6 | 7 8 1 |
| 8 7 4 | 5 9 1 | 3 6 2 |
:---------------+---------------+---------------:
| 2 35 67 | 67 1 8 | 4 35 9 |
| 15 58 178 | 3 4 9 | 6 2 57 |
| 36% 4 9 | 67 2 5 | 8 1 37 |
:---------------+---------------+---------------:
| 7 1 3 | 2 8 4 | 5 9 6 |
| 45-6 568 2 | 9 56 7 | 1 34 348 |
| 45-6 9 68 | 1 56 3 | 2 7 48 |
'---------------'---------------'---------------' |
There is a an xyz-wing that eliminates nothing, but the pincer (6)r1c3 can be transported to (6)r6c1 via (6)r4c3. Thus, we can eliminate 6 from r89c1. This will then reduce to a BUG+1 grid. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Dec 11, 2007 4:39 pm Post subject: |
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| Quote: | | There is a an xyz-wing that eliminates nothing, but the pincer (6)r1c3 can be transported to (6)r6c1 via (6)r4c3. Thus, we can eliminate 6 from r89c1. |
That's very interesting. I had no idea you could transport a pincer to the cell of another original pincer. |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Tue Dec 11, 2007 10:20 pm Post subject: a stinger |
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As per Storm-norm, a simple four step xy-chain eliminates 1 from R1C1.
This opens basic moves which result in a BUG+1 in box 9 which solves the puzzle.
Earl |
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