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Mepham/Stuart Puzzle (Very Hard) 13/05/07

 
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Tue May 15, 2007 6:01 pm    Post subject: Mepham/Stuart Puzzle (Very Hard) 13/05/07 Reply with quote

This one is interesting



Code:
+---+---+---+
|...|.4.|...|
|.23|...|45.|
|..9|5..|2..|
+---+---+---+
|1..|7..|..9|
|.7.|196|.3.|
|6..|..4|..7|
+---+---+---+
|..7|..3|9..|
|.14|...|36.|
|...|.5.|...|
+---+---+---+


See what you think.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed May 16, 2007 12:37 am    Post subject: Reply with quote

What you call "interesting", I call "difficult." I got stuck at the below position. I'm pretty sure I can solve it with a couple of chains, but knowing you, there might be an ALS or two lurking there. Wink

Code:

+----------+---------------+-------------+
| 5  6 1   | 238 4    278  | 78  9   38  |
| 78 2 3   | 689 1678 1789 | 4   5   168 |
| 78 4 9   | 5   36   178  | 2   17  36  |
+----------+---------------+-------------+
| 1  3 28  | 7   28   5    | 6   4   9   |
| 4  7 258 | 1   9    6    | 58  3   28  |
| 6  9 25  | 238 238  4    | 158 128 7   |
+----------+---------------+-------------+
| 2  5 7   | 46  16   3    | 9   18  148 |
| 9  1 4   | 28  278  278  | 3   6   5   |
| 3  8 6   | 49  5    19   | 17  127 124 |
+----------+---------------+-------------+

Play this puzzle online at the Daily Sudoku site
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed May 16, 2007 2:43 pm    Post subject: Mepham/Stuart Puzzle (Very Hard) 13/05/07 Reply with quote

It's true that I saw an ALS ! Very Happy I must be wired that way. I would be interested in other solutions (chains or otherwise)

I reached the same point as you Marty. However, not that it's material but there is a triple in col 4.

Then I saw this ALS



The two locked sets are in green and pink.

The locked common is 1 which means that we now look for all cells that can see the 8's in both sets. These eliminated 8's are highlighted in blue.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed May 16, 2007 3:58 pm    Post subject: Reply with quote

Yes, I agree, you're wired for ALS's. I learned the rule for the ALS some time ago, but never used one because of not really knowing how to look for them efficiently.

I've done maybe 1500 puzzles and (obviously) am still capable of missing triples. Mad
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed May 16, 2007 4:02 pm    Post subject: Reply with quote

Aren't we all ! Laughing

I find with harder puzzles the time spent looking for an ALS is often worth it because I have run out of other options or prefer not to use them (eg UR which is perfectly valid but I don't like 'em).
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Wed May 16, 2007 4:09 pm    Post subject: Reply with quote

Mogulmeister mentioned that he would be interested in other solutions. Well,

Code:

+----------+---------------+-------------+
| 5  6 1   | 238 4    278  | 78  9   38  |
| 78 2 3   | 689 1678 1789 | 4   5   168 |
| 78 4 9   | 5   36   178  | 2   17  36  |
+----------+---------------+-------------+
| 1  3 28  | 7   28   5    | 6   4   9   |
| 4  7 258 | 1   9    6    | 58  3   28  |
| 6  9 25  | 238 238  4    | 158 128 7   |
+----------+---------------+-------------+
| 2  5 7   | 46  16   3    | 9   18  148 |
| 9  1 4   | 28  278  278  | 3   6   5   |
| 3  8 6   | 49  5    19   | 17  127 124 |
+----------+---------------+-------------+

r6c8 is an interesting cell. It is conjugate to r6c7 with respect to 1 and to r9c8 with respect to 2. So, either r6c7 contains 1 or r9c8 contains 2. Whichever applies, 7 must be placed in r9c7 and the puzzle is solved.

someone_somewhere used to like these combinations of conjugates involving different candidates. From memory he called this version a “four star constellation.”

Steve


Last edited by Steve R on Wed May 16, 2007 6:18 pm; edited 2 times in total
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed May 16, 2007 4:29 pm    Post subject: Reply with quote

Many thanks - but did you mean r9c8 instead of r9c7 at the beginning of your explanation Steve ?
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Wed May 16, 2007 4:53 pm    Post subject: Reply with quote

Whoops. Yes.

I have corrected the original, thank you.

Steve
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed May 16, 2007 5:57 pm    Post subject: Reply with quote

Code:
contains 1 or r9c7 contains 2


Steve - this one too ? (pardon the pedantry)
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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Wed May 16, 2007 6:00 pm    Post subject: Reply with quote

Alternative solution in 2 steps:

2-String-Kite for digit 1 in row 3 and column 5 eliminates digit 1 from r7c8, so you can place digit 8 in r7c8.

XY-chain: (8=7)r1c7 - (7=1)r3c8 - (1=2)r6c8 - (2=8)r5c9. Either r1c7=8 or r5c9=8. Eliminate 8 from these 4 cells: r5c7, r6c7, r1c9 & r2c9.

From this point, it's singles all the way.

Ruud
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed May 16, 2007 6:05 pm    Post subject: Reply with quote

Thanks Ruud.
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