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Try this one without the UR!

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keith

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

Posted: Mon Jul 27, 2009 2:19 am Post subject: Try this one without the UR!

I posted this in another thread because it has a big Type 3 UR. But, a solution without the UR is quite interesting!

Code:

Puzzle: M4455254sh(6)
+-------+-------+-------+
| . 4 . | . . . | . . 2 |
| 7 . . | . 8 . | 4 1 . |
| 6 3 . | 5 . . | 7 . . |
+-------+-------+-------+
| . . 3 | 4 . . | . 2 6 |
| . . . | 8 . . | 3 . . |
| . . 2 | . . . | 1 . . |
+-------+-------+-------+
| . . . | 9 . 1 | . . 3 |
| . . . | . 4 7 | . . . |
| . . . | . 6 . | . . 7 |
+-------+-------+-------+

After basics:

Code:

+----------------------+----------------------+----------------------+
| 58 4 58 | 1 7 9 | 6 3 2 |
| 7 2 9 | 6 8 3 | 4 1 5 |
| 6 3 1 | 5 2 4 | 7 89 89 |
+----------------------+----------------------+----------------------+
| 189 7 3 | 4 19 5 | 89 2 6 |
| 1459 1569 456 | 8 19 2 | 3 7 49 |
| 489 89 2 | 7 3 6 | 1 5 489 |
+----------------------+----------------------+----------------------+
| 248 68 7 | 9 5 1 | 28 468 3 |
| 23589 5689 568 | 23 4 7 | 2589 689 1 |
| 123459 159 45 | 23 6 8 | 259 49 7 |
+----------------------+----------------------+----------------------+

Note the <23> UR in C14. The subset is <14589>, eliminating <48> in R7C1.

As I said, try proceeding without using any UR.

Keith

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Mon Jul 27, 2009 3:29 am Post subject:

Code:

.------------------------.------------------------.------------------------.
| 58 4 58 | 1 7 9 | 6 3 2 |
| 7 2 9 | 6 8 3 | 4 1 5 |
| 6 3 1 | 5 2 4 | 7 *89 *89 |
:------------------------+------------------------+------------------------:
| 189 7 3 | 4 19 5 | 89 2 6 |
|1-459 1569 *456 | 8 19 2 | 3 7 49 |
| 489 89 2 | 7 3 6 | 1 5 48-9 |
:------------------------+------------------------+------------------------:
| 248 68 7 | 9 5 1 | 28 468 3 |
| 23589 5689 568 | 23 4 7 | 2589 68-9 1 |
|123-459 159 *45 | 23 6 8 | 259 *49 7 |
'------------------------'------------------------'------------------------'

AIC loop:
(9=4)r5c9 - (4)r5c3 = (4)r9c3 - (4=9)r9c8 - (9)r3c8 = (9)r3c9;
r5c1 <> 4
r9c1 <> 4
r8c8 <> 9
r6c9 <> 9

some singles
naked triple.

Code:

.------------------.------------------.------------------.
|*58 4 -58 | 1 7 9 | 6 3 2 |
| 7 2 9 | 6 8 3 | 4 1 5 |
| 6 3 1 | 5 2 4 | 7 89 89 |
:------------------+------------------+------------------:
|*18 7 3 | 4 19 5 |*89 2 6 |
| 15 56 456 | 8 19 2 | 3 7 49 |
| 49 89 2 | 7 3 6 | 1 5 48 |
:------------------+------------------+------------------:
|*24 68 7 | 9 5 1 |*28 468 3 |
| 239 5689 568 | 23 4 7 | 2589 68 1 |
| 239 1 *45 | 23 6 8 | 259 49 7 |
'------------------'------------------'------------------'

(5=8)r1c1 - (8)r4c1 = (8)r4c7 - (8=2)r7c7 - (2=4)r7c1 - (4=5)r9c3; r1c3 <> 5

Last edited by storm_norm on Mon Jul 27, 2009 4:28 am; edited 1 time in total

keith

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

Posted: Mon Jul 27, 2009 4:20 am Post subject:

I started with a more basic move:

Code:

+----------------------+----------------------+----------------------+
| 58 4 58 | 1 7 9 | 6 3 2 |
| 7 2 9 | 6 8 3 | 4 1 5 |
| 6 3 1 | 5 2 4 | 7 89 89b |
+----------------------+----------------------+----------------------+
| 189 7 3 | 4 19 5 | 89 2 6 |
| 1459 1569 456 | 8 19 2 | 3 7 49# |
| 489% 89 2 | 7 3 6 | 1 5 48-9% |
+----------------------+----------------------+----------------------+
| 248@ 68 7 | 9 5 1 | 28 468@ 3 |
| 23589 5689 568 | 23 4 7 | 2589 689 1 |
| 123459 159 45 | 23 6 8 | 259 49#a 7 |
+----------------------+----------------------+----------------------+

The cells # are a W-wing with pincers <9>, connected by the strong links @% on <4>. If a is <9>, so is b (grouped coloring), eliminating <9> in R6C9.

More, later.

Keith

Marty R.

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

Posted: Mon Jul 27, 2009 4:33 am Post subject:

Quote:

The cells # are a W-wing with pincers <9>, connected by the strong links @% on <4>.

Wouldn't a simpler connection be the 4s in c3?

keith

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

Posted: Mon Jul 27, 2009 5:00 am Post subject:

Marty R. wrote:

Quote:

The cells # are a W-wing with pincers <9>, connected by the strong links @% on <4>.

Wouldn't a simpler connection be the 4s in c3?

Dang! Yes!
And notice the <89> in R3 that makes the <49> a remote pair.

Keith

keith

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

Posted: Mon Jul 27, 2009 4:43 pm Post subject:

So, the <49> are a remote pair, because they are both a W-wing on <4> and on <9>. With a little coloring, they make the same eliminations that Norm's AIC does. I got to here:

Code:

+----------------+----------------+----------------+
| 58 4 58 | 1 7 9 | 6 3 2 |
| 7 2 9 | 6 8 3 | 4 1 5 |
| 6 3 1 | 5 2 4 | 7 89 89 |
+----------------+----------------+----------------+
| 18a 7 3 | 4 19 5 | 89 2 6 |
| 15b 56c 456 | 8 19 2 | 3 7 49 |
| 49 -89 2 | 7 3 6 | 1 5 48 |
+----------------+----------------+----------------+
| 24 68d 7 | 9 5 1 | 28 468 3 |
| 239 5689 568 | 23 4 7 | 2589 68 1 |
| 239 1 45 | 23 6 8 | 259 49 7 |
+----------------+----------------+----------------+

abcd is a four cell chain (extended XY-wing) with pincers <8>.

There is another in R67 <89> that takes out <8> in R7C2. Either one solves it.

Keith

Last edited by keith on Wed Jul 29, 2009 3:39 am; edited 1 time in total

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Tue Jul 28, 2009 6:36 pm Post subject:

keith wrote:

Marty R. wrote:

Quote:

The cells # are a W-wing with pincers <9>, connected by the strong links @% on <4>.

Wouldn't a simpler connection be the 4s in c3?

Dang! Yes!
And notice the <89> in R3 that makes the <49> a remote pair.

Keith

I saw both strong links for the w-wing on 49, but did not realize that made a Remote Pair. I still got the same final eliminations from the W-wings and then completed the puzzle with the xy-wing.

Ted

keith

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

Posted: Wed Jul 29, 2009 3:32 am Post subject:

tlanglet wrote:

I saw both strong links for the w-wing on 49, but did not realize that made a Remote Pair.
Ted

Ted,

So far as I know, there are four ways to make a remote pair:

1. Coloring on the pair: <49> = <49> = <49> = <49>. Any cell that sees both end cells cannot be <4> or <9>.

2. Coloring on one candidate: <49> = <4a> = <4b> = <49>

= is a strong link, a and b are any candidates.

3. A double W-wing:

Code:

/<9a>=<9b>\
<49> <49>
\<4c>=<4d>/

\ / are weak links, c and d are any candidates.

4. Any other method that proves for two cells <49>: One must be <4>, the other must be <9>.

Keith

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