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A Menneske super hard

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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Jan 22, 2011 3:12 pm Post subject: A Menneske super hard

I think there will be a variety of solutions for this one.

Code:

Puzzle: M3842182sh(11)
+-------+-------+-------+
| . . 2 | . . 7 | 6 . . |
| 6 . . | 2 3 . | . . 9 |
| . 8 . | 9 . 6 | . 4 . |
+-------+-------+-------+
| 2 . 1 | . . . | 4 8 . |
| . 9 . | . . . | . 7 . |
| . 6 8 | . . . | 1 . 5 |
+-------+-------+-------+
| . 3 . | 6 . 5 | . 2 . |
| 7 . . | . 8 9 | . . 1 |
| . . 4 | 3 . . | 9 . . |
+-------+-------+-------+

Keith

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Sat Jan 22, 2011 4:29 pm Post subject:

Spent twenty minutes looking for a BUG/MUG move but couldn't find one! So a wing with transport..

Quote:

s-wing(18) transport ; (1)r3c5=r3c1 - (1=8)r7c1 - (8)r7c7=r2c7 - r2c6=r1c4 ; r1c4<>1

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Jan 22, 2011 5:07 pm Post subject:

X-Wing (1) AIC; r2c2<>1 W-Wing (45); r1c2, r2c6<>4

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Jan 22, 2011 6:00 pm Post subject:

After basics:

Code:

+-------------+-------------+-------------+
| 9 145 2 | 18 145 7 | 6 135 38 |
| 6 145 7 | 2 3 148 | 58 15 9 |
| 15 8 3 | 9 15 6 | 27 4 27 |
+-------------+-------------+-------------+
| 2 7 1 | 5 9 3 | 4 8 6 |
| 4 9 5 | 18@ 6 18# | 23 7 23 |
| 3 6 8 | 7 24 24 | 1 9 5 |
+-------------+-------------+-------------+
| 18@ 3 9 | 6 17# 5 | 78 2 4 |
| 7 2 6 | 4 8 9 | 35 35 1 |
| 158 15 4 | 3 127 -12 | 9 6 78 |
+-------------+-------------+-------------+

There is an X-wing on 1 in R37. You don't need it.

Note that R7C1 and R5C4 are a remote pair. You can see that by coloring on 8. So, R7C5 and R5C6 are pincers on 1, and the puzzle is solved. (One of the cells marked @ is 8. Therefore, one of the cells marked # is 1, because of the strong links on 1 in R57.)

Keith Cool

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Jan 22, 2011 6:44 pm Post subject:

keith wrote:

Note that R7C1 and R5C4 are a remote pair. You can see that by coloring on 8. So, R7C5 and R5C6 are pincers on 1, and the puzzle is solved. (One of the cells marked @ is 8. Therefore, one of the cells marked # is 1, because of the strong links on 1 in R57.)

Using the coloring, must one of the @ cells be 8 and the other be 1? If not, the "remote pair" term seems a bit of a stretch.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Jan 22, 2011 7:25 pm Post subject:

ronk wrote:

keith wrote:

Using the coloring, must one of the @ cells be 8 and the other be 1? If not, the "remote pair" term seems a bit of a stretch.

Ron, yes.

The coloring (simple coloring on 8, no grouping or fancy stuff) says that one of the cells is 8, the other is not 8. Ergo, one of them is 1.

So, you can make the Medusa-type extension to the cells # being pincers on 1.

If the @ cells were the pincers of a W-wing (one or both are 1), the extension to # as pincers is not valid.

I noted a few years ago when I wrote my piece on Remote Pairs, W-wings and M-wings, that a remote pair only has to be connected by coloring on one of the digits. I don't think that observation was new, but I had not seen it explicitly stated.

Coloring on 8:

Code:

+-------------+-------------+-------------+
| 9 145 2 | 18% 145 7 | 6 135 38$ |
| 6 145 7 | 2 3 148$| 58% 15 9 |
| 15 8 3 | 9 15 6 | 27 4 27 |
+-------------+-------------+-------------+
| 2 7 1 | 5 9 3 | 4 8 6 |
| 4 9 5 | 18$ 6 18% | 23 7 23 |
| 3 6 8 | 7 24 24 | 1 9 5 |
+-------------+-------------+-------------+
| 18% 3 9 | 6 17 5 | 78$ 2 4 |
| 7 2 6 | 4 8 9 | 35 35 1 |
|158$ 15 4 | 3 127 12 | 9 6 78% |
+-------------+-------------+-------------+

Either all the cells $ are 8, or all the cells % are 8.

Keith

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Jan 22, 2011 11:39 pm Post subject:

keith wrote:

The coloring (simple coloring on 8, no grouping or fancy stuff) says that one of the cells is 8, the other is not 8. Ergo, one of them is 1.

So, you can make the Medusa-type extension to the cells # being pincers on 1.

OK, thanks. I again neglected to consider all the implications of a odd-length conjugate chain. Since there is not a generally accepted way to indicate a conjugate link in nice-loop and AIC notation, this has become a conditioned response for me.

(1)r5c6 = (1-8)r5c4 = (8)r1c4 - (8)r2c6 = (8)r2c7 - (8)r7c7 = (8-1)r7c1 = (1)r7c5 ==> r9c6<>1

Taking this notation literally, r5c6=1 and r7c5=1 could both be true.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Jan 23, 2011 3:47 am Post subject:

Code:

+-----------------------------------------------------+
| 9 145 2 | f18 145 7 | 6 135 e38 |
| 6 145 7 | 2 3 148 | 58 15 9 |
| 15 8 3 | 9 15 6 | 27 4 27 |
|-----------------+-----------------+-----------------|
| 2 7 1 | 5 9 3 | 4 8 6 |
| 4 9 5 | g18 6 h18 | 23 7 23 |
| 3 6 8 | 7 24 24 | 1 9 5 |
|-----------------+-----------------+-----------------|
| b18 3 9 | 6 a17 5 | 78 2 4 |
| 7 2 6 | 4 8 9 | 35 35 1 |
| c158 15 4 | 3 127 2-1 | 9 6 d78 |
+-----------------------------------------------------+
# 36 eliminations remain

What Keith considers to be a "conjugate" relationship, I consider to be two concurrent chains. His use of coloring simply forces all inferences on <8> to use strong links:

Code:

(1=8)r7c1 - r9c1 = r9c9 - r1c9 = r1c4 - (8=1)r5c4 => peers of r7c1 & r5c4 <> 1
( -8)r7c1 = r9c1 - r9c9 = r1c9 - r1c4 = (8 )r5c4 => peers of r7c1 & r5c4 <> 8

This is the foundation for Keith's general Remote Pair.

Combine the second chain with the strong links on <1> in [r5] and [r7], and you have Keith's extension:

Code:

(1)r7c5 = (1-8)r7c1 = r9c1 - r9c9 = r1c9 - r1c4 = (8-1)r5c4 = (1)r5c6 => r9c6<>1

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Jan 23, 2011 6:26 am Post subject:

File under: Beating a dead horse.

After the X-wing:

Code:

+-------------+-------------+-------------+
| 9 145 2 | 18 45 7 | 6 135 38 |
| 6 145 7 | 2 3 148 | 58 15 9 |
| 15 8 3 | 9 15 6 | 27 4 27 |
+-------------+-------------+-------------+
| 2 7 1 | 5 9 3 | 4 8 6 |
| 4 9 5 | 18g 6 -18h | 23 7 23 |
| 3 6 8 | 7 24 24 | 1 9 5 |
+-------------+-------------+-------------+
| 18b 3 9 | 6 17a 5 | 78 2 4 |
| 7 2 6 | 4 8 9 | 35 35 1 |
| 58 15 4 | 3 27 12j | 9 6 78 |
+-------------+-------------+-------------+

b and g are remote pair or W-wing pincers on 1. Extending b-a-j, 1 is eliminated from h.

The distinction between remote pair pincers and W-wing pincers is important in puzzles like this, which occur every two years or so. Laughing

Quote:

Combine the second chain with the strong links on <1> in [r5] and [r7], and you have Keith's extension

Actually, Danny proposed this sort of stacked skyscraper (that he calls Keith's extension) some time ago. I previously thought I found one, but he disagreed. Maybe he agrees with this one.

(Who is that third person?)

Keith

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Jan 23, 2011 9:47 am Post subject:

along the same lines

Code:

+-------------+-----------------+---------------+
| 9 145 2 | 18 145 7 | 6 135 38 |
| 6 145 7 | 2 3 14(8) | 5(8) 15 9 |
| 15 8 3 | 9 15 6 | 27 4 27 |
+-------------+-----------------+---------------+
| 2 7 1 | 5 9 3 | 4 8 6 |
| 4 9 5 | 18 6 (18) | 23 7 23 |
| 3 6 8 | 7 24 24 | 1 9 5 |
+-------------+-----------------+---------------+
| 18 3 9 | 6 (17) 5 | (78) 2 4 |
| 7 2 6 | 4 8 9 | 35 35 1 |
| 158 15 4 | 3 127 2-1 | 9 6 78 |
+-------------+-----------------+---------------+

(1=7)r7c5 - (7=8)r7c7 - (8)r2c7 = (8)r2c6 - (8=1)r5c6; r9c6 <> 1

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Jan 23, 2011 5:24 pm Post subject:

Poor ole` horse!

Code:

+-----------------------------------------------------+
| 9 145 2 | 18 145 7 | 6 135 38 |
| 6 145 7 | 2 3 148 | 58 15 9 |
| 15 8 3 | 9 15 6 | 27 4 27 |
|-----------------+-----------------+-----------------|
| 2 7 1 | 5 9 3 | 4 8 6 |
| 4 9 5 | 18 6 18 | 23 7 23 |
| 3 6 8 | 7 24 24 | 1 9 5 |
|-----------------+-----------------+-----------------|
| 18 3 9 | 6 17 5 | 78 2 4 |
| 7 2 6 | 4 8 9 | 35 35 1 |
| 158 15 4 | 3 127 12 | 9 6 78 |
+-----------------------------------------------------+
# 36 eliminations remain

This puzzle is balanced on a razor's edge waiting to be cracked after basics. Here are six chains using just <1> & <8> that crack it using just four SI's. The first two are W-Wing extensions. The last two are internally-extended S-Wings.

Code:

(8=1)r7c1 - r3c1 = r3c5 - (1=8)r1c4 - r1c9 = (8)r9c9 => r7c7,r9c1<>8
(8=1)r1c4 - r3c5 = r3c1 - (1=8)r7c1 - r7c7 = (8)r2c7 => r1c9,r2c6<>8

(1=8)r5c6 - r2c6 = r2c7 - r7c7 = (8-1)r7c1 = (1)r7c5 => r9c6<>1
(1=8)r1c4 - r1c9 = r2c7 - r7c7 = (8-1)r7c1 = (1)r7c5 => r13c5<>1

(1)r3c1 = r3c5 - (1=8)r1c4 - r1c9 = r2c7 - r7c7 = (8)r7c1 => r7c1<>1
(1)r3c5 = r3c1 - (1=8)r7c1 - r7c7 = r9c9 - r1c9 = (8)r1c4 => r1c4<>1

ronk

Joined: 07 May 2006
Posts: 398

Posted: Mon Jan 24, 2011 12:28 pm Post subject:

keith wrote:

After the X-wing:

Code:

If a "remote pair" doesn't yield eliminations for both digit values of the pair, as in this case, IMO it's a distinction without a difference.

royalina

Joined: 21 Feb 2011
Posts: 4

Posted: Mon Feb 21, 2011 6:43 am Post subject:

you can make the Medusa-type extension to the cells # being pincers on 1. 。。。。

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