dailysudoku.com :: View topic - Another Menneske, with a tough first step!

dailysudoku.com
Discussion of Daily Sudoku puzzles

FAQ

Memberlist

Usergroups

Profile

Another Menneske, with a tough first step!

dailysudoku.com Forum Index -> Other puzzles

View previous topic :: View next topic

Author

Message

keith

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

Posted: Sun Oct 18, 2009 3:48 pm Post subject: Another Menneske, with a tough first step!

Code:

Puzzle: M6798876sh(17)
+-------+-------+-------+
| . . . | . 8 5 | 7 . . |
| . . . | . . . | . . . |
| . 3 9 | 6 . . | . 4 . |
+-------+-------+-------+
| . 6 . | . . . | . 3 . |
| 5 . . | . . . | 2 . . |
| 3 9 . | . 7 . | . . 4 |
+-------+-------+-------+
| . 2 . | . . 3 | . . . |
| . . . | 7 . . | . 1 9 |
| 6 . 8 | . . 4 | . . 5 |
+-------+-------+-------+

Keith

Marty R.

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

Posted: Sun Oct 18, 2009 8:23 pm Post subject:

Two steps.

Quote:

Finned X-Wing on 8 exposed a W-Wing on 12. The latter created locked candidates on 1 which finished it off

keith

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

Posted: Sun Oct 18, 2009 8:36 pm Post subject:

Marty R. wrote:

Two steps.

Quote:

Finned X-Wing on 8 exposed a W-Wing on 12. The latter created locked candidates on 1 which finished it off

This is from Multi-step Marty Question

My solution is much more complicated!
Keith Very Happy

keith

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

Posted: Sun Oct 18, 2009 8:43 pm Post subject:

Marty, That is very elegant! Keith

DonM

Joined: 15 Sep 2009
Posts: 51

Posted: Sun Oct 18, 2009 9:30 pm Post subject:

Keith, what is the starting point for this 1st step? Is it the SSTS position? There are the usual singles and whatnot from the position above.

keith

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

Posted: Mon Oct 19, 2009 12:39 am Post subject:

Don,

After basics, I get here:

Code:

+-------------------+-------------------+-------------------+
| 12 14 6 | 1234 8 5 | 7 9 123 |
| 1278 148 5 | 12349 12349 1279 | 168 68 12368 |
| 1278 3 9 | 6 12 127 | 5 4 128 |
+-------------------+-------------------+-------------------+
| 18 6 47 | 12458 1245 128 | 9 3 178 |
| 5 18 47 | 13489 13469 1689 | 2 678 1678 |
| 3 9 2 | 18 7 168 | 168 5 4 |
+-------------------+-------------------+-------------------+
| 9 2 1 | 58 56 3 | 4 678 678 |
| 4 5 3 | 7 26 268 | 68 1 9 |
| 6 7 8 | 19 19 4 | 3 2 5 |
+-------------------+-------------------+-------------------+

By first step, I meant, after basics.

I will post my solution in a few minutes.

Keith

Marty R.

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

Posted: Mon Oct 19, 2009 12:42 am Post subject:

Quote:

That is very elegant!

Thank you. Keep in mind the old saying, "Even a blind pig finds an acorn once in a while." Laughing

keith

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

Posted: Mon Oct 19, 2009 1:05 am Post subject:

Code:

+-------------------+-------------------+-------------------+
| 12 14 6 |-1234 8 5 | 7 9 123 |
| 1278 148 5 |-12349 -1-2349 1279| 168 68 12368 |
| 1278 3 9 | 6 12a 127 | 5 4 128 |
+-------------------+-------------------+-------------------+
| 18 6 47 |-1245-8 -1-245 128 | 9 3 178 |
| 5 18 47 |-134-89 -134-69 1689| 2 678 1678 |
| 3 9 2 | 18d 7 168 | 168 5 4 |
+-------------------+-------------------+-------------------+
| 9 2 1 | 58e 56e 3 | 4 678 678 |
| 4 5 3 | 7 26f 2-68 | 68 1 9 |
| 6 7 8 | 19c 19b 4 | 3 2 5 |
+-------------------+-------------------+-------------------+

abcdef..a is an XY-loop. a and f are pincers of an XY-chain, but since they are in the same house, they make a reversible loop. Any two adjacent cells in the chain are pincers in their common candidate. Therefore, you can make the eliminations shown.

Maybe my notation in the diagram is not entirely correct, but it should show:

Quote:

One of R3C5 and R8C5 must be <2>.
One of R8C5 and R7C5 must be <6>.
One of R7C5 and R7C4 must be <5>.
One of R7C4 and R6C4 must be <8>.
One of R6C4 and R9C4 must be <1>.
One of R9C4 and R9C5 must be <9>.
One of R9C5 and R3C5 must be <1>.

Thus:

R2C5 - cannot contain <2> because of R3C5 and R8C5.
R4C5 - cannot contain <2> because of R3C5 and R8C5.
R8C6 - cannot contain <6> because of R8C5 and R7C5.
R5C5 - cannot contain <6> because of R8C5 and R7C5.
R4C4 - cannot contain <8> because of R7C4 and R6C4.
R5C4 - cannot contain <8> because of R7C4 and R6C4.
R1C4 - cannot contain <1> because of R6C4 and R9C4.
R2C4 - cannot contain <1> because of R6C4 and R9C4.
R4C4 - cannot contain <1> because of R6C4 and R9C4.
R5C4 - cannot contain <1> because of R6C4 and R9C4.
R2C5 - cannot contain <1> because of R9C5 and R3C5.
R4C5 - cannot contain <1> because of R9C5 and R3C5.
R5C5 - cannot contain <1> because of R9C5 and R3C5.

Leading to here:

Code:

+-------------------+-------------------+-------------------+
| 12 14 6 | 234 8 5 | 7 9 123 |
| 1278 148 5 | 2349 349 1279 | 168 68 12368 |
| 1278 3 9 | 6 12 127 | 5 4 128 |
+-------------------+-------------------+-------------------+
| 18 6 47 | 245 45 128 | 9 3 178 |
| 5 18 47 | 349 349 1689 | 2 678 1678 |
| 3 9 2 | 18 7 168 | 168 5 4 |
+-------------------+-------------------+-------------------+
| 9 2 1 | 58 56 3 | 4 678 678 |
| 4 5 3 | 7 26 28 | 68 1 9 |
| 6 7 8 | 19 19 4 | 3 2 5 |
+-------------------+-------------------+-------------------+

which still has a few advanced steps to a solution.

What amazes me is that Marty's finned 8 X-wing is still in the above grid, and is a completely different path. Here it is:

Code:

+-------------------+-------------------+-------------------+
| 12 14 6 | 234 8 5 | 7 9 123 |
| 1278 148 5 | 2349 349 1279 | 168 68 12368 |
| 1278 3 9 | 6 12 127 | 5 4 128 |
+-------------------+-------------------+-------------------+
| 18 6 47 | 245 45 12-8 | 9 3 178 |
| 5 18 47 | 349 349 16-89 | 2 678 1678 |
| 3 9 2 | 18# 7 168@ | 168@ 5 4 |
+-------------------+-------------------+-------------------+
| 9 2 1 | 58 56 3 | 4 678 678 |
| 4 5 3 | 7 26 28@ | 68@ 1 9 |
| 6 7 8 | 19 19 4 | 3 2 5 |
+-------------------+-------------------+-------------------+

Either the X-wing @ is true, or # is true. Either way, R45C6 cannot be 8.

Keith

Last edited by keith on Mon Oct 19, 2009 1:07 am; edited 1 time in total

keith

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

Posted: Mon Oct 19, 2009 1:06 am Post subject:

Marty R. wrote:

Quote:

That is very elegant!

Thank you. Keep in mind the old saying, "Even a blind pig finds an acorn once in a while." Laughing

In this case, more like a truffle!

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Mon Oct 19, 2009 1:59 am Post subject:

After basics and Marty's excellent finned X-Wing, there's his W-Wing and this XY-Chain:

Code:

XY-Chain a-b-c-d-e
+-----------------------------------------------------------------------+
| 12 14 6 | 1234 8 5 | 7 9 123 |
| 1278 148 5 | 12349 12349 1279 | 168 68 12368 |
| 1278 3 9 | 6 12 127 | 5 4 128 |
|-----------------------+-----------------------+-----------------------|
| 18 6 47 | 12458 145-2 a12 | 9 3 178 |
| 5 18 47 | 13489 13469 169 | 2 678 167 |
| 3 9 2 | b18 7 168 | 168 5 4 |
|-----------------------+-----------------------+-----------------------|
| 9 2 1 | c58 d56 3 | 4 678 678 |
| 4 5 3 | 7 e26 68-2 | 68 1 9 |
| 6 7 8 | 19 19 4 | 3 2 5 |
+-----------------------------------------------------------------------+
# 83 eliminations remain

In addition, there's the shortest SIN (Single Implication Network) that I recall seeing in some time:

Code:

[r4c6]=1
/ \
[r8c6]=2 => contradiction; => [r8c6]<>2
\ /
[r6c6]=8 [r6c4]=1
+-----------------------------------------------------------------------+
| 12 14 6 | 1234 8 5 | 7 9 123 |
| 1278 148 5 | 12349 12349 1279 | 168 68 12368 |
| 1278 3 9 | 6 12 127 | 5 4 128 |
|-----------------------+-----------------------+-----------------------|
| 18 6 47 | 12458 1245 12 | 9 3 178 |
| 5 18 47 | 13489 13469 169 | 2 678 167 |
| 3 9 2 | 18 7 168 | 168 5 4 |
|-----------------------+-----------------------+-----------------------|
| 9 2 1 | 58 56 3 | 4 678 678 |
| 4 5 3 | 7 26 268 | 68 1 9 |
| 6 7 8 | 19 19 4 | 3 2 5 |
+-----------------------------------------------------------------------+
# 83 eliminations remain

Yes, it can be represented as a short chain, but the simplicity is lost.

DonM

Joined: 15 Sep 2009
Posts: 51

Posted: Mon Oct 19, 2009 10:47 pm Post subject:

Code:

Here's a 2-step pattern-solving ALS-chain alternative (rc=restricted common):

Step 1: Dual-linked ALS:
Set A(1589)r679c4 -> rc5 & rc9 -> Set B(12569)r3789c5

Elims: 1 in r1245c4, 1 in r245c5, 8 in r45c4, 2 in r24c5, 6 in r5c5

Step 2: 3-set ALS chain:
Set A(123489)r12569c4 -> rc2 -> Set B(123459)r23459c5 -> rc5 -> Set C(2568)r7c5/r8c56

Thus: r7c4<>8=5
stte

tlanglet

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

Posted: Thu Oct 22, 2009 1:14 am Post subject:

Marty R. wrote:

Two steps.

Quote:

Finned X-Wing on 8 exposed a W-Wing on 12. The latter created locked candidates on 1 which finished it off

Great move Marty! I love to see those finned and Kraken solutions.

Ted

Display posts from previous:

	dailysudoku.com Forum Index -> Other puzzles	All times are GMT
Page 1 of 1

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum