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LAT/freep 11-sep-09 + telegraph

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sun Sep 13, 2009 8:31 pm    Post subject: LAT/freep 11-sep-09 + telegraph Reply with quote

Freep/LAT

002530100750004000006020000014000060300000509000000720000090600000800012008067300

Code:

+-------+-------+-------+
| . . 2 | 5 3 . | 1 . . |
| 7 5 . | . . 4 | . . . |
| . . 6 | . 2 . | . . . |
+-------+-------+-------+
| . 1 4 | . . . | . 6 . |
| 3 . . | . . . | 5 . 9 |
| . . . | . . . | 7 2 . |
+-------+-------+-------+
| . . . | . 9 . | 6 . . |
| . . . | 8 . . | . 1 2 |
| . . 8 | . 6 7 | 3 . . |
+-------+-------+-------+

Play online

--------
Daily telegraph

003109700080020000700300005050036000006905800000000040900002000000050070008604200

Code:

+-------+-------+-------+
| . . 3 | 1 . 9 | 7 . . |
| . 8 . | . 2 . | . . . |
| 7 . . | 3 . . | . . 5 |
+-------+-------+-------+
| . 5 . | . 3 6 | . . . |
| . . 6 | 9 . 5 | 8 . . |
| . . . | . . . | . 4 . |
+-------+-------+-------+
| 9 . . | . . 2 | . . . |
| . . . | . 5 . | . 7 . |
| . . 8 | 6 . 4 | 2 . . |
+-------+-------+-------+

Play online
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Kdelle



Joined: 20 Mar 2008
Posts: 59
Location: Hudson, NH

PostPosted: Mon Sep 14, 2009 7:23 pm    Post subject: Stuck on Freep/LAT posted by Norm Reply with quote

I got this far and am impossibly stuck. Did anyone try it with success? Am I missing something obvious? Any little hint will help! Thanks.

Kathy


Code:

+---------------+-------------+-------------+
| 489  489  2   | 5   3  689  | 1  79   467 |
| 7    5    139 | 69  18 4    | 2  389  68  |
| 1489 3489 6   | 7   2  189  | 49 3589 458 |
+---------------+-------------+-------------+
| 259  1    4   | 29  7  59   | 8  6    3   |
| 3    268  7   | 26  18 168  | 5  4    9   |
| 589  689  59  | 34  45 3689 | 7  2    1   |
+---------------+-------------+-------------+
| 145  34   135 | 134 9  2    | 6  78   78  |
| 6    7    39  | 8   45 35   | 49 1    2   |
| 1249 249  8   | 14  6  7    | 3  59   45  |
+---------------+-------------+-------------+

Play this puzzle online at the Daily Sudoku site
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Mon Sep 14, 2009 10:18 pm    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

Kdelle wrote:
I got this far and am impossibly stuck.
Code:
 *-----------------------------------------------------------*
 | 489   489   2     | 5     3     689   | 1     79    467   |
 | 7     5     139   | 69   *18    4     | 2     389   68    |
 | 1489  3489  6     | 7     2    *189   | 49    3589  458   |
 |-------------------+-------------------+-------------------|
 | 259   1     4     | 29    7     59    | 8     6     3     |
 | 3     268   7     | 26   *18   *168   | 5     4     9     |
 | 589   689   59    | 34    45    3689  | 7     2     1     |
 |-------------------+-------------------+-------------------|
 | 145   34    135   | 134   9     2     | 6     78    78    |
 | 6     7     39    | 8     45    35    | 49    1     2     |
 | 1249  249   8     | 14    6     7     | 3     59    45    |
 *-----------------------------------------------------------*
(1)r3c6=(1=8)r2c5=(8=1)r5c5=(1)r5c6=(1)r3c6=>r3c6=1


I don't know what this is or even if it is legal but it works.
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Kdelle



Joined: 20 Mar 2008
Posts: 59
Location: Hudson, NH

PostPosted: Mon Sep 14, 2009 10:30 pm    Post subject: Reply with quote

(1)r3c6=(1=8)r2c5=(8=1)r5c5=(1)r5c6=(1)r3c6=>r3c6=1

I don't think I understand the notation. Could you say it in words?
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Mon Sep 14, 2009 11:40 pm    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

arkietech wrote:
I don't know what this is or even if it is legal but it works.

Dan, it's a good thing that it works because I don't believe that it is legal.
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Tue Sep 15, 2009 1:28 am    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

daj95376 wrote:
arkietech wrote:
I don't know what this is or even if it is legal but it works.

Dan, it's a good thing that it works because I don't believe that it is legal.

Why does this not apply?
THEOREM 3:
At the discontinuity of a simple nice loop where 2 links with strong inference of same labels meet, the digit that labels the links can be fixed in the cell between the links.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Sep 15, 2009 5:46 am    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

Kdelle wrote:
I got this far and am impossibly stuck. Did anyone try it with success? Am I missing something obvious? Any little hint will help! Thanks.

Kathy


Code:

+---------------+-------------+-------------+
| 489  489  2   | 5   3  689  | 1  79   467 |
| 7    5    139 | 69  18 4    | 2  389  68  |
| 1489 3489 6   | 7   2  189  | 49 3589 458 |
+---------------+-------------+-------------+
| 259  1    4   | 29  7  59   | 8  6    3   |
| 3    268  7   | 26  18 168  | 5  4    9   |
| 589  689  59  | 34  45 3689 | 7  2    1   |
+---------------+-------------+-------------+
| 145  34   135 | 134 9  2    | 6  78   78  |
| 6    7    39  | 8   45 35   | 49 1    2   |
| 1249 249  8   | 14  6  7    | 3  59   45  |
+---------------+-------------+-------------+

Play this puzzle online at the Daily Sudoku site


looks like you caught the skyscraper on 1's
and the xy-wing on {3,5,9} which removed the 5 in r6c6.
these techniques work because of the relationships between the candidates. once these relationships are more easily seen by the mind's eye then the sky is the limit for finding more.

anyways, I found these next two moves.
1...
Code:
+-------------------+---------------+---------------+
| 489    489   2    | 5    3   689  | 1   79    467 |
| 7      5     13-9 | 69   18  4    | 2   389   68  |
| 1489   3489  6    | 7    2   189  | 49  3589  458 |
+-------------------+---------------+---------------+
| 29(5)  1     4    | 29   7   9(5) | 8   6     3   |
| 3      268   7    | 26   18  168  | 5   4     9   |
| 89-5   689   (59) | 34   45  3689 | 7   2     1   |
+-------------------+---------------+---------------+
| 145    34    135  | 134  9   2    | 6   78    78  |
| 6      7     (39) | 8    45  (35) | 49  1     2   |
| 1249   249   8    | 14   6   7    | 3   59    45  |
+-------------------+---------------+---------------+

loop...(9=3)r8c3 - (3=5)r8c6 - (5)r4c6 = (5)r4c1 - (5=9)r6c3; r2c3 <> 9, r4c1 <> 5.

2...
Code:
+-------------------+---------------+-------------------+
| 489   489   2     | 5    3   689  | 1     79      467 |
| 7     5     -3(1) | 69   18  4    | 2     89(3)   68  |
| 1489  3489  6     | 7    2   189  | 49    89(35)  458 |
+-------------------+---------------+-------------------+
| 259   1     4     | 29   7   59   | 8     6       3   |
| 3     268   7     | 26   18  168  | 5     4       9   |
| 89    689   (59)  | 34   45  3689 | 7     2       1   |
+-------------------+---------------+-------------------+
| 145   34    3(15) | 134  9   2    | 6     78      78  |
| 6     7     3(9)  | 8    45  35   | 4(9)  1       2   |
| 1249  249   8     | 14   6   7    | 3     (59)    45  |
+-------------------+---------------+-------------------+

(1)r2c3 = (1-5)r7c3 = (5-9)r6c3 = (9)r8c3 - (9)r8c7 = (9-5)r9c8 = (5-3)r3c8 = (3)r2c8; r2c3 <> 3

singles to end.
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Tue Sep 15, 2009 10:07 am    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

arkietech wrote:
Why does this not apply?
THEOREM 3:
At the discontinuity of a simple nice loop where 2 links with strong inference of same labels meet, the digit that labels the links can be fixed in the cell between the links.

Code:
 *-----------------------------------------------------------*
 | 489   489   2     | 5     3     689   | 1     79    467   |
 | 7     5     139   | 69   *18    4     | 2     389   68    |
 | 1489  3489  6     | 7     2    *189   | 49    3589  458   |
 |-------------------+-------------------+-------------------|
 | 259   1     4     | 29    7     59    | 8     6     3     |
 | 3     268   7     | 26   *18   *168   | 5     4     9     |
 | 589   689   59    | 34    45    3689  | 7     2     1     |
 |-------------------+-------------------+-------------------|
 | 145   34    135   | 134   9     2     | 6     78    78    |
 | 6     7     39    | 8     45    35    | 49    1     2     |
 | 1249  249   8     | 14    6     7     | 3     59    45    |
 *-----------------------------------------------------------*

A) Your original chain.
B) Correcting for incorrect signs.
C) Removing extraneous use of <8>.
D) Removing incorrect conclusion.

Code:
A) (1)r3c6 = (1=8)r2c5 = (8=1)r5c5 = (1)r5c6 = (1)r3c6 => r3c6=1
B) (1)r3c6 = (1-8)r2c5 = (8-1)r5c5 = (1)r5c6 - (1)r3c6 => r3c6=1
C) (1)r3c6 = (1  )r2c5 - (  1)r5c5 = (1)r5c6 - (1)r3c6 => r3c6=1
D) (1)r3c6 = (1  )r2c5 - (  1)r5c5 = (1)r5c6 - (1)r3c6

You have a continuous loop in <1>. Unfortunately, all of your weak inferences are strong links, so you don't have any eliminations.

I'm assuming that your Theorem 3 doesn't apply because you don't have a discontinuity -- one link to [r3c6] is a strong inference and the second link is a weak inference.
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Tue Sep 15, 2009 10:50 am    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

storm_norm wrote:
Code:
+-------------------+---------------+---------------+
| 489    489   2    | 5    3   689  | 1   79    467 |
| 7      5     13-9 | 69   18  4    | 2   389   68  |
| 1489   3489  6    | 7    2   189  | 49  3589  458 |
+-------------------+---------------+---------------+
| 29(5)  1     4    | 29   7   9(5) | 8   6     3   |
| 3      268   7    | 26   18  168  | 5   4     9   |
| 89-5   689   (59) | 34   45  3689 | 7   2     1   |
+-------------------+---------------+---------------+
| 145    34    135  | 134  9   2    | 6   78    78  |
| 6      7     (39) | 8    45  (35) | 49  1     2   |
| 1249   249   8    | 14   6   7    | 3   59    45  |
+-------------------+---------------+---------------+

continuous loop...(9=3)r8c3 - (3=5)r8c6 - (5)r4c6 = (5)r4c1 - (5=9)r6c3 - loop; r2c3<>9, r6c1<>5

-or-

Code:
+-------------------+---------------+---------------+
| 489    489   2    | 5    3   689  | 1   79    467 |
| 7      5     13-9 | 69   18  4    | 2   389   68  |
| 1489   3489  6    | 7    2   189  | 49  3589  458 |
+-------------------+---------------+---------------+
| 295    1     4    | 29   7   95   | 8   6     3   |
| 3      268   7    | 26   18  168  | 5   4     9   |
| 89-5   689   (59) | 34  (45) 3689 | 7   2     1   |
+-------------------+---------------+---------------+
| 145    34    135  | 134  9   2    | 6   78    78  |
| 6      7     (93) | 8   (54) (35) | 49  1     2   |
| 1249   249   8    | 14   6   7    | 3   59    45  |
+-------------------+---------------+---------------+

continuous XY-Loop: (9=3)r8c3 - (3=5)r8c6 - (5=4)r8c5 - (4=5)r6c5 - (5=9)r6c3 - loop; r2c3<>9, r6c1<>5

Note: Cell candidates ordered to reflect strong inferences in cells. Any candidate on both the left side and right side in a unit can have that candidate eliminated in other cells of that unit. Thus, the elimination of <5> in [r6] and the elimination of <9> in [c3].

There aren't any eliminations for:

    <3> in [r8]

    <5> in [r8] or [b8]

    <4> or <5> in [c5] because they form a Naked Pair. This is a good reason why basic and simpler eliminations should be performed before looking for a chain!
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Tue Sep 15, 2009 12:44 pm    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

daj95376 wrote:
You have a continuous loop in <1>. Unfortunately, all of your weak inferences are strong links, so you don't have any eliminations.

Thanks Danny Shocked I have a lot to learn. All the inferences looked strong to me.
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Kdelle



Joined: 20 Mar 2008
Posts: 59
Location: Hudson, NH

PostPosted: Tue Sep 15, 2009 1:02 pm    Post subject: Reply with quote

(1)r2c3 = (1-5)r7c3 = (5-9)r6c3 = (9)r8c3 - (9)r8c7 = (9-5)r9c8 = (5-3)r3c8 = (3)r2c8; r2c3 <> 3

Norm or Danny,

I still don't really understand Norm's second move because I can't read the notation. What I did do was look at the cells involved and I think I'm seeing it backwards. If I assume r2c3 is 3, then the 3 in r3c8 forces a 9 in r8c7 which forces a 3 in r8c3, which is forbidden, so r2c3 must be 1.

In Norm's notation, I read (1)r2c3 to mean assume r2c3 to be 1, but I don't really think that's what it means. Can either of you clear this up for me? I'm very appreciative of your time. Thanks,

Kathy
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Sep 15, 2009 5:52 pm    Post subject: Reply with quote

Kdelle wrote:
(1)r2c3 = (1-5)r7c3 = (5-9)r6c3 = (9)r8c3 - (9)r8c7 = (9-5)r9c8 = (5-3)r3c8 = (3)r2c8; r2c3 <> 3

Norm or Danny,

I still don't really understand Norm's second move because I can't read the notation. What I did do was look at the cells involved and I think I'm seeing it backwards. If I assume r2c3 is 3, then the 3 in r3c8 forces a 9 in r8c7 which forces a 3 in r8c3, which is forbidden, so r2c3 must be 1.

In Norm's notation, I read (1)r2c3 to mean assume r2c3 to be 1, but I don't really think that's what it means. Can either of you clear this up for me? I'm very appreciative of your time. Thanks,

Kathy


Kathy,
hi, how are you?
the first strong inference in my chain... (1)r2c3 = (1)r7c3
it doesn't mean that I am assuming r2c3 is 1.
instead this inference means that neither of the 1's can both be false.

the symbol "-" means that the candidates on either side cannot both be true.

with this in mind, see what happens when you read the chain from left to right not assuming that r2c3 is true, but instead trying it when the 1 in r2c3 is false. I think you will get better results.

you can do the same if you start with the right most candidate.

Danny,
thanx for the correction. blindness on my part.
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Tue Sep 15, 2009 6:30 pm    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

arkietech wrote:
daj95376 wrote:
You have a continuous loop in <1>. Unfortunately, all of your weak inferences are strong links, so you don't have any eliminations.

Thanks Danny Shocked I have a lot to learn. All the inferences looked strong to me.

All of your links are strong, but your inferences altenate. That's why I changed the signs! BTW: I seldom think in terms of links anymore. They are just a Sudopedia side-note in my chains reference file.

===== ===== ===== Basic Chain Terminology and Notation ===== ===== =====

Code:
Strong Inference (SI):  ~A =>  B
Weak   Inference (WI):   A => ~B

Code:
(SI):  e.g., ( bilocation  (n)a = (n)b ) or ( bivalue cell  (m=n)c )
(WI):  e.g., ( peers       (n)d - (n)e ) or ( ?-value cell  (m-n)f )

Code:
bilocation   (n)a = (n)b:  if [a] is not 'n', then [b] is     'n'
bivalue cell    (m=n)c  :  if [c] is not 'm', then [c] is     'n'

peers        (n)d - (n)e:  if [d] is     'n', then [e] is not 'n'
?-value cell    (m-n)f  :  if [f] is     'm', then [f] is not 'n'

Sudopedia: a strong link can be used as either a strong inference or a weak inference, but a weak link can only be used for weak inference.


Last edited by daj95376 on Tue Sep 15, 2009 6:43 pm; edited 1 time in total
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Kdelle



Joined: 20 Mar 2008
Posts: 59
Location: Hudson, NH

PostPosted: Tue Sep 15, 2009 6:39 pm    Post subject: Reply with quote

storm_norm wrote:
Kdelle wrote:
(1)r2c3 = (1-5)r7c3 = (5-9)r6c3 = (9)r8c3 - (9)r8c7 = (9-5)r9c8 = (5-3)r3c8 = (3)r2c8; r2c3 <> 3

Norm or Danny,

I still don't really understand Norm's second move because I can't read the notation. What I did do was look at the cells involved and I think I'm seeing it backwards. If I assume r2c3 is 3, then the 3 in r3c8 forces a 9 in r8c7 which forces a 3 in r8c3, which is forbidden, so r2c3 must be 1.

In Norm's notation, I read (1)r2c3 to mean assume r2c3 to be 1, but I don't really think that's what it means. Can either of you clear this up for me? I'm very appreciative of your time. Thanks,

Kathy


Kathy,
hi, how are you?
the first strong inference in my chain... (1)r2c3 = (1)r7c3
it doesn't mean that I am assuming r2c3 is 1.
instead this inference means that neither of the 1's can both be false.

the symbol "-" means that the candidates on either side cannot both be true.

with this in mind, see what happens when you read the chain from left to right not assuming that r2c3 is true, but instead trying it when the 1 in r2c3 is false. I think you will get better results.

you can do the same if you start with the right most candidate.

Danny,
thanx for the correction. blindness on my part.


Norm, thanks. I see it now. I think I was confused by the "-" WITHIN the (.....). Not really understanding the notation makes for massive muddle sometimes! You guys are a great help!

Kathy
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Tue Sep 15, 2009 7:11 pm    Post subject: Re: Stuck on Freep/LAT posted by Norm Reply with quote

daj95376 wrote:

a strong link can be used as either a strong inference or a weak inference, but a weak link can only be used for weak inference.

I finally see it! Thanks. I found the following on Sudopedia
Quote:
For this to work, the links must alternate strong and weak. You may be inclined to write the following chain:

A - B = C = D = E - F
However, this chain uses the wrong inference between premises C and D. This might be illustrated by showing the list of implications:

If A is true, B is false.
If B is false, C is true.
If C is false, D is true.
If D is false, E is true.
If E is true, F is false.
There is no proper connection between the 3rd line and those preceding and succeeding it. If the strong link between C and D is one of those types of strong link that is also a weak link, we can convert it to a weak inference to write a correct chain:

A - B = C - D = E - F
Alternating inference guarantees that the logic is sound from the first to the last node in the chain.

A false implication must be connected with a strong inference
A true implication must be connected with a weak inference

Look out I am getting dangerous! Very Happy
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Sep 15, 2009 9:11 pm    Post subject: Reply with quote

telegraph puzzle

basics get it to here...
step 1
Code:
+-------------------+------------+------------------+
| 5      24(6)  3   | 1  (46)  9 | 7     268  4(28) |
| -4(6)  8      149 | 5  2     7 | 3     169  149   |
| 7      12     129 | 3  6(4)  8 | 6(4)  129  5     |
+-------------------+------------+------------------+
| 8      5      12  | 4  3     6 | 19    129  7     |
| (24)   124    6   | 9  7     5 | 8     3    1(2)  |
| 3      9      7   | 2  8     1 | 5     4    6     |
+-------------------+------------+------------------+
| 9      3      5   | 7  1     2 | 6(4)  68   (48)  |
| 246    246    24  | 8  5     3 | 19    7    19    |
| 1      7      8   | 6  9     4 | 2     5    3     |
+-------------------+------------+------------------+

(4=2)r5c1 - (2)r5c9 = (2-8)r1c9 = (8-4)r7c9 = (4)r7c7 - (4)r3c7 = (4)r3c5 - (4=6)r1c5 - (6)r1c2 = (6)r2c1; r2c1 <> 4
------
step 2
this step is interesting because it uses an almost x-wing
Code:
+---------------------+----------+----------------+
| 5      (24)   3     | 1  46  9 | 7   68     248 |
| 6      8      149   | 5  2   7 | 3   19     149 |
| 7      1(2)   19(2) | 3  46  8 | 46  19(2)  5   |
+---------------------+----------+----------------+
| 8      5      1(2)  | 4  3   6 | 19  19(2)  7   |
| -2(4)  12(4)  6     | 9  7   5 | 8   3      12  |
| 3      9      7     | 2  8   1 | 5   4      6   |
+---------------------+----------+----------------+
| 9      3      5     | 7  1   2 | 46  68     48  |
| (24)   6      4-2   | 8  5   3 | 19  7      19  |
| 1      7      8     | 6  9   4 | 2   5      3   |
+---------------------+----------+----------------+

notice the 2's in r34
if the 2 in r3c2 is not there then you are left with a x-wing r34c38
that x-wing would eliminate the 2 in r8c3.
if the x-wing is false, that leaves the 2 in r3c2. if that 2 is true, then you can follow the logic around and the 2 in r8c3 is still false.

[x-wing(2)r34c38] = (2)rc2 - (2=4)r1c2 - (4)r5c2 = (4)r5c1 - (4=2)r8c1; r8c3 <> 2

but also notice that if we stop the chain at r5c1, then that 2 is also eliminated.

singles follow.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Sep 16, 2009 8:16 pm    Post subject: Reply with quote

I know some of you are familiar with Andrew Stuarts online solver and like to check your progress there.
here are the links to open these puzzles on his page.


LAT/FREEP 11-sep-09


Daily telegraph 11-sep-09
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Sep 17, 2009 11:58 am    Post subject: Reply with quote

Telegraph puzzle - A different route:

after basics, m-wing:

Code:

+--------------------------+--------------------------+--------------------------+
| 5      -246     3        | 1       46      9        | 7       268     248*     |
| 46      8       149      | 5       2       7        | 3       169     149      |
| 7       12*     129      | 3       46      8        | 46     1-29     5        |
+--------------------------+--------------------------+--------------------------+
| 8       5       12       | 4       3       6        | 19      129     7        |
| 24      124#    6        | 9       7       5        | 8       3       12#      |
| 3       9       7        | 2       8       1        | 5       4       6        |
+--------------------------+--------------------------+--------------------------+
| 9       3       5        | 7       1       2        | 46      68      48       |
| 246     246     24       | 8       5       3        | 19      7       19       |
| 1       7       8        | 6       9       4        | 2       5       3        |
+--------------------------+--------------------------+--------------------------+


using the strong link (1) in row 5, r3c2 and r1c9 form the pincers to remove 2 from r1c2 and r3c8.

After some cleanup, a UR (19) r23c38 with strong link (9) in c3, which removes 9 from r2c8:

Code:

+--------------------------+--------------------------+--------------------------+
| 5       46      3        | 1       46      9        | 7       28      28       |
| 46#     8      -19       | 5       2       7        | 3       16*-9   149      |
| 7       12      129      | 3       46      8        | 46      19      5        |
+--------------------------+--------------------------+--------------------------+
| 8       5       12*      | 4       3       6        | 19     -129     7        |
| 24#     124     6        | 9       7       5        | 8       3       12       |
| 3       9       7        | 2       8       1        | 5       4       6        |
+--------------------------+--------------------------+--------------------------+
| 9       3       5        | 7       1       2        | 46      68      48       |
| 26      26      4        | 8       5       3        | 19      7       19       |
| 1       7       8        | 6       9       4        | 2       5       3        |
+--------------------------+--------------------------+--------------------------+


In the resulting grid, a short xy-chain - a.k.a. extended xy wing Wink - removes 1 from cells r2c3 and r4c8
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