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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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 Posted: Sat Oct 16, 2010 9:00 pm Post subject: Canadian Hard or VH? |
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This is one from my Canadian newspaper that NEVER has Very Hard level puzzles. So I have avoided wings and things - but cannot find a basic solution. What's up eh!
| Code: |
+-------+-------+-------+
| 3 . . | . . 5 | . . . |
| 2 1 . | 8 . . | 6 . . |
| . 9 7 | . . 1 | . . . |
+-------+-------+-------+
| 9 . 6 | . 8 . | . . . |
| 1 4 . | . . . | . 8 6 |
| . . . | . 1 . | 4 . 3 |
+-------+-------+-------+
| . . . | 2 . . | 3 9 . |
| . . 9 | . . 7 | . 5 8 |
| . . . | 9 . . | . . 4 |
+-------+-------+-------+
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Oct 16, 2010 9:28 pm Post subject: |
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Our paper never has a puzzle that can't be solved with basics.
But I'm stuck on yours at this point, that is, stuck as far as further basics go.
| Code: |
+----------------+-----------+--------------+
| 3 68 48 | 7 26 5 | 18 124 9 |
| 2 1 45 | 8 9 34 | 6 347 57 |
| 4568 9 7 | 34 26 1 | 58 234 25 |
+----------------+-----------+--------------+
| 9 237 6 | 34 8 234 | 157 127 1257 |
| 1 4 23 | 5 7 23 | 9 8 6 |
| 578 2578 258 | 6 1 9 | 4 27 3 |
+----------------+-----------+--------------+
| 4578 578 1458 | 2 45 6 | 3 9 17 |
| 46 36 9 | 1 34 7 | 2 5 8 |
| 57 2357 1235 | 9 35 8 | 17 6 4 |
+----------------+-----------+--------------+
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Play this puzzle online at the Daily Sudoku site |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Oct 16, 2010 10:30 pm Post subject: |
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| Code: | .------------------.------------------.------------------.
| 3 68 48 | 7 26 5 | 18 124 9 |
| 2 1 45 | 8 9 34 | 6 347 57 |
| 4568 9 7 | 34 26 1 | 58 234 25 |
:------------------+------------------+------------------:
| 9 237 6 | 34 8 234 | 157 127 1257 |
| 1 4 23 | 5 7 23 | 9 8 6 |
| 578 2578 258 | 6 1 9 | 4 27 3 |
:------------------+------------------+------------------:
| 4578 578 1458 | 2 45 6 | 3 9 17 |
| 46 36 9 | 1 34 7 | 2 5 8 |
| 57 2357 1235 | 9 35 8 | 17 6 4 |
'------------------'------------------'------------------' |
| Quote: | | (1=8)r1c7 - (8)r3c7 = (8-5)r3c1 = (5)r2c3 - (5=7)r2c9 - (7)r7c9 = (7)r9c7; r9c7 <> 1 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Oct 16, 2010 11:22 pm Post subject: |
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| Norm, why not shorten the chain to r1c7, r3c7, r2c9 and r7c9? |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun Oct 17, 2010 2:25 am Post subject: |
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| Marty R. wrote: | | Norm, why not shorten the chain to r1c7, r3c7, r2c9 and r7c9? |
that works too. |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Sun Oct 17, 2010 6:54 pm Post subject: |
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My husband and I are stuck on this puzzle too.  This is not just a basics puzzle. Does anyone have any solutions for it. |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Sun Oct 17, 2010 7:22 pm Post subject: |
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| I just want to add that this puzzle is the one that Earl used to post every Saturday. For some reason he hasn't been posting it anymore. In our newspaper it is listed as a 6 star. It is never a just 'basics' puzzle. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Oct 18, 2010 12:52 am Post subject: |
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| Sheila, I don't see anything beyond the XY-Chain noted above. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Oct 18, 2010 10:10 pm Post subject: |
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Two ANPs does the trick.
| Code: | +----------------+-----------+--------------+
| 3 68 48 | 7 26 5 | 18 124 9 |
| 2 1 45 | 8 9 34 | 6 347 57 |
| 4568 9 7 | 34 26 1 | 58 234 25 |
+----------------+-----------+--------------+
| 9 237 6 |*34 8 *234 | 157 127 1257 |
| 1 4 23 | 5 7 23 | 9 8 6 |
| 578 2578 258 | 6 1 9 | 4 27 3 |
+----------------+-----------+--------------+
| 4578 578 1458 | 2 45 6 | 3 9 17 |
| 46 36 9 | 1 34 7 | 2 5 8 |
| 57 2357 1235 | 9 35 8 | 17 6 4 |
+----------------+-----------+--------------+ |
Look at the cells r4c46 marked *. If the extra (or fin) 2 in r4c6 is false, then we have a NP(34), but if the fin is true then the NP is destroyed; one of these conditions, the NP or the fin, MUST be true. The trick is to determine if both make a common deletion.
If the NP is true, then r4c2<>3
If the fin is true then one possibility is as follows:
If r4c6=2, then r4c89<>2, then r6c8=2, then r13c8<>2, then r3c9=2, then r3c5<>2=6, then r1c5<>6, then r1c2=6, then r8c2<>6=3, then r4c2<>3
Thus, both the NP and the fin (2)r4c6 have a common deletion, r4c2<>3, and it may be removed!
In notational form, this could be expressed as:
ANP(34=2)r4c46-(2)r4c89=(2)r6c8-(2)r13c8=(2)r3c9-(2=6)r3c5-(6)r1c5=(6)r1c2-(6=3)r8c2; r4c2<>3
This brings us to the following code.
| Code: | *-----------------------------------------------------------*
| 3 68 48 | 7 26 5 | 18 124 9 |
| 2 1 45 | 8 9 34 | 6 347 57 |
| 4568 9 7 | 34 26 1 | 58 234 25 |
|-------------------+-------------------+-------------------|
| 9 27 6 | 34 8 34 | 157 *127 1257 |
| 1 4 3 | 5 7 2 | 9 8 6 |
| 578 2578 258 | 6 1 9 | 4 *27 3 |
|-------------------+-------------------+-------------------|
| 4578 578 1458 | 2 45 6 | 3 9 17 |
| 46 36 9 | 1 34 7 | 2 5 8 |
| 57 2357 125 | 9 35 8 | 17 6 4 |
*-----------------------------------------------------------* |
Here we have another ANP pattern in cells r46c8, marked *. Either the NP(27) is true or the fin (1)r4c8 must be true.
So we again look at the deletions provided by both conditions to determine if any common deletions exist.
If NP(27) is true, then r4c9<>2,r13c8<>2,r4c79<>7,r2c8<>7
If the fin is true then one possibility is as follows:
If r4c8=1, then r4c9<>1, then r7c9=1, then r9c7<>1, then r9c3=1, then r9c3<>2, then r9c2=2, then r4c2=7, then r4c79<>7
The only common deletions by both the NP(27)r46c8 and the fin (1)r4c8 are r4c79<>7, which completes the puzzle
In notational form, this could be expressed as:
ANP(27=1)r46c8-(1)r4c9=(1)r7c9-(1)r9c7=(1-2)r9c3=(2)r9c2-(2=7)r4c2; r4c79<>7
Ted |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Oct 23, 2010 11:13 pm Post subject: |
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After basics: | Code: | +----------------+----------------+----------------+
| 3 68 48 | 7 26 5 | 18 124 9 |
| 2 1 45 | 8 9 34 | 6 347 57a |
| 4568 9 7 | 34 26 1 | 58 234 25 |
+----------------+----------------+----------------+
| 9 237 6 | 34 8 234 | 157b 127 1257 |
| 1 4 23 | 5 7 23 | 9 8 6 |
| 578 2578 258 | 6 1 9 | 4 27 3 |
+----------------+----------------+----------------+
| 4578 578 1458 | 2 45 6 | 3 9 1-7 |
| 46 36 9 | 1 34 7 | 2 5 8 |
| 57 2357 1235 | 9 35 8 | 17c 6 4 |
+----------------+----------------+----------------+ |
M-wing:
5 in a forces 5 (not 7) in b forces 7 in c. a and c are pincers in 7.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Oct 24, 2010 3:08 am Post subject: |
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| Quote: | | Code: | +----------------+----------------+----------------+
| 3 68 48 | 7 26 5 | 18 124 9 |
| 2 1 45 | 8 9 34 | 6 347 57a |
| 4568 9 7 | 34 26 1 | 58 234 25 |
+----------------+----------------+----------------+
| 9 237 6 | 34 8 234 | 157b 127 1257 |
| 1 4 23 | 5 7 23 | 9 8 6 |
| 578 2578 258 | 6 1 9 | 4 27 3 |
+----------------+----------------+----------------+
| 4578 578 1458 | 2 45 6 | 3 9 1-7 |
| 46 36 9 | 1 34 7 | 2 5 8 |
| 57 2357 1235 | 9 35 8 | 17c 6 4 |
+----------------+----------------+----------------+ |
M-wing: 5 in a forces 5 (not 7) in b forces 7 in c. a and c are pincers in 7. |
This is, I think, a good tutorial example for M-wings. You should understand the concepts of coloring and of strong or conjugate links.
The M-wing has its name because it is the simplest case of Medusa coloring. You DO NOT have to understand Medusa coloring to understand an M-wing.
Start with a bivalue cell a, XY (R2C9 57. X is 5, Y is 7.).
Step 1: Can you find another cell, b, where X in a forces X in b? (Yes, R4C7)
Step 2: Do the candidates for cell b also include Y? (Yes, the candidates are 157.)
Step 3: Is there a cell, c, that is a strong link on Y with b? (Yes, if R4C7 is not 7, then R9C7 is 7.)
If yes, a and c (R2C9 and R9C7) are pincers on Y (7).
To summarize the logic:
| Quote: | a is X or a is Y.
If a is X, b is X.
If b is X, c is Y.
a and c are pincers on Y. |
Keith |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Sun Oct 24, 2010 8:56 pm Post subject: |
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Thanks Keith & Tlanglet. I will print this off and my husband and I will try to understand it. Hopefully we will with some study. 
Sheila |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Oct 25, 2010 3:22 am Post subject: |
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Sheila,
The original ideas are summarized here:
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
They may be of interest.
The recipe I have outlined in this thread allows you to discover what some have called a "generalized half M-wing". They are fairly common and, I think, not too difficult to find (with this recipe).
I will continue to point out examples as they come up.
Best wishes,
Keith |
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