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A more difficult one

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keith

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

Posted: Sat Oct 18, 2008 8:59 pm Post subject: A more difficult one

This weekend's puzzles have been pretty easy. Here is one of those curiously tough Menneskes:

Code:

Puzzle: M2735861vh(0)
+-------+-------+-------+
| . 5 . | 1 . 2 | 4 3 . |
| . . . | . 6 . | . 7 . |
| 8 . . | 5 . . | . . . |
+-------+-------+-------+
| 1 6 . | 7 . . | 8 . . |
| 7 . . | . . . | . . 9 |
| . . 8 | . . 4 | . 1 7 |
+-------+-------+-------+
| 5 . . | 2 . . | . . 6 |
| 2 8 . | . 7 . | . . . |
| . . . | 8 . 6 | . 2 . |
+-------+-------+-------+

Keith

ravel

Joined: 21 Apr 2006
Posts: 536

Posted: Sat Oct 18, 2008 9:54 pm Post subject:

Interesting puzzle, starts with a UR again (this time i won Smile

)

Code:

*--------------------------------------------------------------------*
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 12349 | 34 6 8 | 1259 7 125 |
| 8 12349 12349 | 5 34 7 | 1269 69 12 |
|----------------------+----------------------+----------------------|
| 1 6 #23459 | 7 235 359 | 8 #45 2345 |
| 7 234 #2345 | 36 8 1 | 2356 #456 9 |
| 39 239 8 | 369 235 4 | 2356 1 7 |
|----------------------+----------------------+----------------------|
| 5 13479 1349 | 2 134 39 | 379 8 6 |
| 2 8 6 | 349 7 359 | 1359 459 1345 |
| 349 13479 1349 | 8 1345 6 | 3579 2 345 |
*--------------------------------------------------------------------*

UR 45, you can eliminate 4 both from r5c3 and r5c8 (because r5c8=4 => r4c3=4)
[Edit:]This was a mistake, for r5c3<>4 you first have to eliminate 5 from r5c7 (swordfish)

Then i had skyscraper, kite, xyz-wing, 2 finned x-wings, 3-link coloring, swordfish, 2 4-cell xy-wings and another UR Exclamation

Last edited by ravel on Sun Oct 19, 2008 10:00 pm; edited 1 time in total

keith

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

Posted: Sat Oct 18, 2008 10:04 pm Post subject:

Wow I am still stuck in the weeds! Staring at that useless <39> W-wing. Keith

Marty R.

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

Posted: Sat Oct 18, 2008 11:07 pm Post subject:

This is pretty ridiculous for a puzzle rated VH from him. I've used five techniques and each just eliminated one candidate with no further value.

Code:

+-----------------+-------------+---------------+
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 12349 | 34 6 8 | 1259 7 125 |
| 8 12349 1234 | 5 34 7 | 1269 69 12 |
+-----------------+-------------+---------------+
| 1 6 23459 | 7 235 359 | 8 45 234 |
| 7 234 2345 | 36 8 1 | 2356 456 9 |
| 39 239 8 | 369 25 4 | 2356 1 7 |
+-----------------+-------------+---------------+
| 5 13479 1349 | 2 134 39 | 379 8 6 |
| 2 8 6 | 349 7 359 | 139 459 1345 |
| 349 13479 1349 | 8 135 6 | 3579 2 345 |
+-----------------+-------------+---------------+

Play this puzzle online at the Daily Sudoku site

ravel

Joined: 21 Apr 2006
Posts: 536

Posted: Sat Oct 18, 2008 11:42 pm Post subject:

You can make the UR 45 eliminations her. But probably the swordfish on 5 is needed also (i know, you dont like to look for them).

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Oct 19, 2008 12:03 am Post subject:

The start of this puzzle is definitely for fishermen!

Code:

XYZ-Wing, Swordfish, Franken Swordfish, and finned Franken Swordfish leaving:
+-----------------------------------------------------------------------+
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 1239 1239 | 34 6 8 | 1259 7 125 |
| 8 12349 1234 | 5 34 7 | 1269 69 12 |
|-----------------------+-----------------------+-----------------------|
| 1 6 23459 | 7 23 359 | 8 45 234 |
| 7 234 2345 | 36 8 1 | 236 456 9 |
| 39 239 8 | 369 25 4 | 2356 1 7 |
|-----------------------+-----------------------+-----------------------|
| 5 13479 1349 | 2 134 39 | 379 8 6 |
| 2 8 6 | 349 7 359 | 139 459 134 |
| 349 1379 139 | 8 135 6 | 3579 2 345 |
+-----------------------------------------------------------------------+
# 92 eliminations remain

Marty R.

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

Posted: Sun Oct 19, 2008 12:12 am Post subject:

ravel wrote:

You can make the UR 45 eliminations her. But probably the swordfish on 5 is needed also (i know, you dont like to look for them).

You're right, I don't like to look for them. Probably because I don't know when to look for them, looking for them is very tedious and it amounts to too much work for too little return. But I did play your swordfish and haven't gotten anywhere with it.

I also don't understand the UR, even though you provided an explanation (I'm just doing great on this puzzle!) Embarassed

tlanglet

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

Posted: Sun Oct 19, 2008 1:34 am Post subject:

I am also lost on the UR 45. I only see one strong link; on <5> in col3. For me, if r5c8=4 => r4c8=5 => r4c3 not 5 => r5c3=5 (due to the strong link). Why does r4c3=4 Ted

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Oct 19, 2008 2:06 am Post subject:

While you're waiting on ravel's clarification.

Code:

results of [r5c3]=4 due to strong links on (5) in [c3] and [c6]
*--------------------------------------------------------------------*
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 1239 | 34 6 8 | 1259 7 125 |
| 8 12349 1239 | 5 34 7 | 1269 69 12 |
|----------------------+----------------------+----------------------|
| 1 6 *5 | 7 23 39 | 8 *4 23 |
| 7 23 *4 | 36 8 1 | 236 *5 9 |
| 39 239 8 | 369 235 4 | 236 1 7 |
|----------------------+----------------------+----------------------|
| 5 13479 139 | 2 134 39 | 379 8 6 |
| 2 8 6 | 349 7 *5 | 139 9 134 |
| 349 13479 139 | 8 134 6 | 3579 2 345 |
*--------------------------------------------------------------------*

Code:

results of [r5c8]=4 due to grouped strong links on (4) and strong link on (5) in [c3]
*--------------------------------------------------------------------*
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 1239 | 34 6 8 | 1259 7 125 |
| 8 12349 1239 | 5 34 7 | 1269 69 12 |
|----------------------+----------------------+----------------------|
| 1 6 *4 | 7 23 39 | 8 *5 23 |
| 7 23 *5 | 36 8 1 | 236 *4 9 |
| 39 239 8 | 369 235 4 | 236 1 7 |
|----------------------+----------------------+----------------------|
| 5 13479 139 | 2 134 39 | 379 8 6 |
| 2 8 6 | 349 7 359 | 1359 9 1345 |
| 349 13479 139 | 8 1345 6 | 3579 2 345 |
*--------------------------------------------------------------------*

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Sun Oct 19, 2008 5:15 am Post subject:

Marty wrote:

You're right, I don't like to look for [Swordfish].

Well then, consider looking for Finned X-Wings (with fin transports) since they are usually lurking with the Swordfish. Also, consider multi-coloring. Here, the Swordfish eliminates <5>s in r4c59, r5c7 and r8c79. Those same eliminations can be accomplished using the alternate (and possibly easier to spot) approaches.

Consider the Finned X-Wing in r29 with Fin r9c5. The Fin tranports first to r4c6 to eliminate <5> in r4c9. Then, it transports to r5c3 to eliminate <5> in r5c7.

Next, consider the c68 Finned X-Wing. It removes <5> from r4c9 directly and from both r4c5 and r4c9 after transporting the Fin from r5c8 to r4c3.

The Finned X-Wing in r69 eliminates <5> in r8c7. (This can also be done with a Kite pivoting in box 5, a Kite being a simple case of multi-coloring.)

That leaves just the <5> in r8c9 that we haven't yet dealt with. There are a couple of possibilities. One is to notice the "wrong way" Skyscraper in r26 and transport the otherwise useless pincer at r6c5 to r8c6. This is also just multi-coloring (or Color Wing), as marked below:

Code:

+-------------------+-----------------+------------------+
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 12349 | 34 6 8 |@125a9 7 @125A |
| 8 12349 12349 | 5 34 7 | 1269 69 12 |
+-------------------+-----------------+------------------+
| 1 6 23459 | 7 235 359 | 8 45 2345 |
| 7 234 2345 | 36 8 1 | 2356 456 9 |
| 39 239 8 | 369 @235B 4 |@235b6 1 7 |
+-------------------+-----------------+------------------+
| 5 13479 1349 | 2 134 39 | 379 8 6 |
| 2 8 6 | 349 7 @35B9 | 1359 459 #134-5 |
| 349 13479 1349 | 8 @1345b 6 | 3579 2 345 |
+-------------------+-----------------+------------------+

In multi-coloring terms, we have a weak "ab" bridge in c7 with the strong "AB" pair that traps that r8c9 <5>.

But, we can also continue the Fin transport from that c68 Finned X-Wing. We left the Fin at r4c3. Now, we tranport it to r8c6 (via r6c5) and eliminate the <5>s from r8c79 both at once! Notice that the Fin has been transported onto one of the X-Wing cells. That might seem weird; but, it's perfectly acceptable.

So... if finding those Swordfish makes you cross-eyed, then look for these other critters. They're almost always there. You need more steps than the single Swordfish. But, the end result is the same.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Oct 19, 2008 6:26 am Post subject:

this should be the grid after xyz-wing
swordfish on 5
and skyscraper on 4

Code:

.---------------------.---------------------.---------------------.
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 12349 | 34 6 8 | 1259 7 125 |
| 8 12349 1234-9 | 5 34 7 | 1269 69* 12 |
:---------------------+---------------------+---------------------:
| 1 6 23459* | 7 23 359* | 8 45 234 |
| 7 234 2345 | 36 8 1 | 236 456 9 |
| 39 239 8 |369* 25 4 | 2356 1 7 |
:---------------------+---------------------+---------------------:
| 5 13479 1349 | 2 134 39 | 379 8 6 |
| 2 8 6 |349* 7 359 | 139 459* 134 |
| 349 13479 1349 | 8 135 6 | 3579 2 345 |
'---------------------'---------------------'---------------------'

then if you do some coloring on 9, you can chain together a couple strong links and eliminate the 9 in r3c3.

next is a long chain starting in r6c1 and ending in r5c4

Code:

.---------------------.---------------------.---------------------.
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 12349 | 34 6 8 | 1259 7 125 |
| 8 12349 1234 | 5 34 7 | 1269 #69 12 |
:---------------------+---------------------+---------------------:
| 1 6 23459 | 7 23 359 | 8 45 234 |
| 7 234 2345 |#36 8 1 | 236 #456 9 |
|#39 239 8 |#369 25 4 |#2356 1 7 |
:---------------------+---------------------+---------------------:
| 5 13479 1349 | 2 134 39 | 379 8 6 |
| 2 8 6 |#349 7 359 | 139 #459 134 |
| 349 13479 1349 | 8 135 6 | 3579 2 345 |
'---------------------'---------------------'---------------------'

(3=9)r6c1-(9)r6c4=(9)r98c4-(9)r8c8=(9-6)r3c8=(6)r5c8-(6)r6c7=(6)r6c4-(6=3)r5c4; r5c2 and r5c3 is not 3
if anyone can verify that.

if not then I can eliminate some 4's with two other chains with a grouped link.

(4)r2c1=(4)r9c1-(4)r9c9={(4)r8c8|r8c9}-(4)r8c4=(4)r2c4; r2c2|r2c3 <>4

(4)r9c9={(4)r8c8|r8c9}-(4)r8c4=(4)r2c4-(4)r2c1=(4)r9c9; r9c2|r9c3 <> 4

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Sun Oct 19, 2008 6:41 am Post subject:

Since ravel beat me to it, I ignored that UR. (Also, while the elimination of <4> from r5c8 is fairly evident to me, the elimination of <4> from r5c3 involves too much "what if" for my taste.)

After the Swordfish, a 4 Skyscraper, an XYZ-Wing that removes <3> from r6c5, and multi-coloring/ERs that remove <9> from r3c3, I was here:

Code:

+--------------------+---------------+----------------+
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 12349 #123-49 | 34 6 8 | 1259 7 125 |
| 8 @12349 @1234 | 5 @34 7 | 1269 69 12 |
+--------------------+---------------+----------------+
| 1 6 f23459 | 7 23 359 | 8 45 234 |
| 7 @234 @2345 | 36 8 1 | 236 F456 9 |
| 39 239 8 | 369 25 4 | 2356 1 7 |
+--------------------+---------------+----------------+
| 5 @13479 @1349 | 2 @134 39 | 379 8 6 |
| 2 8 6 | 349 7 359 | 139 459 134 |
| 349 13479 #13-49 | 8 135 6 | 3579 2 345 |
+--------------------+---------------+----------------+

There's a Finned Swordfish in r357 (marked) with the r5c8 Fin, "F", transported to r4c3, "f", eliminating <4>s in r29c3. Then,

Code:

+--------------------+---------------+----------------+
| 6 5 7 | 1 9 2 | 4 3 8 |
| 349 #123-49 1239 | 34 6 8 | 1259 7 125 |
| 8 @12349 F1234 | 5 @34 7 | 1269 69 12 |
+--------------------+---------------+----------------+
| 1 6 23459 | 7 23 359 | 8 45 234 |
| 7 f234 2345 | 36 8 1 | 236 456 9 |
| 39 239 8 | 369 25 4 | 2356 1 7 |
+--------------------+---------------+----------------+
| 5 @13479 F1349 | 2 @134 39 | 379 8 6 |
| 2 8 6 | 349 7 359 | 139 459 134 |
| 349 #13-479 139 | 8 135 6 | 3579 2 345 |
+--------------------+---------------+----------------+

there is the Finned X-Wing in r37 with the 2-celled Fin at r37c3, "F", transported to r5c2, "f", eliminating <4>s in r29c2.

Those are the steps of, perhaps, general interest. After that, I resorted to Medusa multi-coloring and found 3 AICs that chipped away at cell r4c3 until the puzzle was solved:

(2)r4c3 - (2)r4c5=(2-5)r6c5=(5-9)r4c6=(9-2)r4c3; r4c3<>2

(5)r4c3 - (5)r5c3=(5-6)r5c8=(6-9)r3c8=(9)r8c8 - (9)r8c4=(9)r6c4 - (9)r4c6=(9-5)r4c3; r4c3<>5

And, after a bit of simplification:

(4)r4c3 - (4)r5c2=(4-6)r5c8=(6-9)r3c8=(9)r8c8 - (9)r8c4=(9)r6c4 - (9)r4c6=(9-4)r4c3; r4c3<>4

You'll notice that the last two AICs are mostly identical, which is sorta interesting. In any case, Medusa Multi-coloring worked with moderate ease.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Oct 19, 2008 6:54 am Post subject:

I knew I was on the right track Asellus, that is awesome how those two eliminations in r4c3 follow that 9 around like that. sweetness!! Last edited by storm_norm on Sun Oct 19, 2008 7:06 am; edited 1 time in total

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Sun Oct 19, 2008 7:00 am Post subject:

Norm wrote:

(3=9)r6c1-(9)r6c4=(9)r98c4-(9)r8c8=(9-6)r3c8=(6)r5c8-(6)r6c7=(6)r6c4-(6=3)r5c4; r5c2 and r5c3 is not 3
if anyone can verify that.

With pleasure!

Since there is no <9> in r9c4, we can fix one of your cell references. Also, there is no need for the detour through the <6>s in r6. Plus, r6c4 is also a victim. So, your AIC can be written as:

(3)r5c23|r6c4 - (3=9)r6c1 - (9)r6c4=(9)r8c4 - (9)r8c8=(9-6)r3c8=(6)r5c8 - (6=3)r5c4 - (3)r5c23|r6c4; r5c23|r6c4<>3

Your <4> eliminations are the same as mine, but viewed differently. By the way, instead of "{(4)r8c8|r8c9}" you can just write "(4)r8c89". It's simpler that way.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Oct 19, 2008 7:07 am Post subject:

I just think the more I write out the less confusing it is to see. just me I guess.

Marty R.

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

Posted: Sun Oct 19, 2008 3:47 pm Post subject:

Asellus wrote:

Marty wrote:

You're right, I don't like to look for [Swordfish].

Code:

Asellus,

I am familiar, or so I thought, with the techniques you mention with the exception of fin transport. Unfortunately, I don't see a Finned X-Wing in r29, based on what I though a Finned X-Wing was. I can see an "almost" X-Wing on 5 in boxes 39, but if the fin is in r9c5, well, I thought a fin had to be in the same box.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Oct 19, 2008 6:02 pm Post subject:

Asellus wrote:

Consider the sd-Kraken X-Wing in r29 with Fin r9c5. The Fin tranports first to r4c6 to eliminate <5> in r4c9. Then, it transports to r5c3 to eliminate <5> in r5c7.

===== ===== ===== =====

Basic Swordfish can be described by the number of times the candidate appears in each unit (row/column). Fortunately, very few basic Swordfish have three occurrences of the candidate in all three units. In this puzzle, there is a (223) Swordfish in r269. If you didn't happen to see it, you can still (easily) find eliminations by using single-digit forcing nets on the rows with only two of the candidate cells. (This often works with Jellyfish as well.)

Code:

[r2c9]=5 => [r48c9]<>5
[r2c7]=5 [r69c7]<>5 [r6c5]=5 [r9c5]<>5 [r9c9]=5 => [r48c9]<>5
+-----------------------------------+
| . 5 . | . . . | . . . |
| . . . | . . . | 5 . 5 |
| . . . | 5 . . | . . . |
|-----------+-----------+-----------|
| . . 5 | . 5 5 | . 5 -5 |
| . . 5 | . . . | 5 5 . |
| . . . | . 5 . | 5 . . |
|-----------+-----------+-----------|
| 5 . . | . . . | . . . |
| . . . | . . 5 | 5 5 -5 |
| . . . | . 5 . | 5 . 5 |
+-----------------------------------+

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Sun Oct 19, 2008 8:20 pm Post subject:

Marty wrote:

I thought a fin had to be in the same box.

It does if you ignore transporting. However, with transporting in the picture, the Fin can be located anywhere. It just needs to be in an either/or relationship with the potential X-Wing (to be a legitimate Fin). Then, if it can be transported to a location where it "sees" candidates that would also be eliminated by that potential X-Wing, those candidates can be eliminated.

ravel

Joined: 21 Apr 2006
Posts: 536

Posted: Sun Oct 19, 2008 8:41 pm Post subject:

Asellus wrote:

(Also, while the elimination of <4> from r5c8 is fairly evident to me, the elimination of <4> from r5c3 involves too much "what if" for my taste.)

Oh, you are very right. This was a mistake by me. When i hurried through the puzzle, i overlooked, that this one did need the swordfish (or transported finned x-wing) elimination of 5 in r5c7 first. Sorry Embarassed

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