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Impossible Menneske No. 02

 
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keith



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

PostPosted: Tue Feb 26, 2013 11:38 pm    Post subject: Impossible Menneske No. 02 Reply with quote

Code:
 M6912298 Impossible (5997)
+-------+-------+-------+
| . . . | . 8 . | 5 . 7 |
| . 6 . | . . . | . . . |
| 4 . . | 7 . . | . 1 . |
+-------+-------+-------+
| . . 1 | . . . | . 8 9 |
| . . . | . . 5 | 2 . . |
| 7 . . | . 9 . | 4 . . |
+-------+-------+-------+
| . . . | . . 6 | . . 4 |
| . . 2 | 1 . . | . 9 . |
| . . 6 | 5 . . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Ask, ye shall receive!

Keith


Last edited by keith on Sun Mar 17, 2013 4:29 am; edited 1 time in total
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Wed Feb 27, 2013 10:39 am    Post subject: Reply with quote

#1. r56c9=1=r79c7, r5c3=4, r6c89=5=r4c12, r2c3=7
#2. Chain[2] : Finned XWing(6R16) : r1c8=r1c4-r6c4=r6c89 :=> -6r5c8

Strongest digits : 5,6,1 whose X Chains are weakly coupled in r23c5 and r6c89.
They enter the following loop :
Code:
+----------------------+---------------------------+-----------------------+
| 1239    1239    39   | 2349(6)  8         12349  | 5     234(6)  7       |
| 123589  6       7    | 2349     -234(15)  12349  | 389   234     238     |
| 4       23589   3589 | 7        -23(56)   239    | 3689  1       2368    |
+----------------------+---------------------------+-----------------------+
| 2356    235     1    | 2346     23467     2347   | 367   8       9       |
| 3689    389     4    | 368      367(1)    5      | 2     37      36(1)   |
| 7       238     38   | 2368     9         1238   | 4     -3(56)  -36(15) |
+----------------------+---------------------------+-----------------------+
| 13589   135789  3589 | 2389     237       6      | 1378  2357    4       |
| 358     34578   2    | 1        347       3478   | 3678  9       3568    |
| 1389    134789  6    | 5        2347      234789 | 1378  237     238     |
+----------------------+---------------------------+-----------------------+
Loop[6] : 6r1c4=(6-5)r3c5=(5-1)r2c5=1r5c5-1r5c9=(1-5)r6c9=(5-6)r6c8=6r1c8 @
:=> r3c5=56=r6c8,r2c5=15=r6c9

Adding the chain 5r3c3=5r7c3-5r7c8=5r6c8 to the loop solves the loop because
r6c9=5->no 5 in Box 2 :=> r6c8=5.
Interpretation :
Code:
+------------------------+--------------------------+--------------------+
| 1239    1239    39     | 2349(6)  8        12349  | 5     234(6)  7    |
| 123589  6       7      | 2349     12345    12349  | 389   234     238  |
| 4       23589   389(5) | 7        23-5(6)  239    | 3689  1       2368 |
+------------------------+--------------------------+--------------------+
| 2356    235     1      | 2346     23467    2347   | 367   8       9    |
| 3689    389     4      | 368      1367     5      | 2     37      136  |
| 7       238     38     | 2368     9        1238   | 4     3(56)   1356 |
+------------------------+--------------------------+--------------------+
| 13589   135789  389(5) | 2389     237      6      | 1378  237(5)  4    |
| 358     34578   2      | 1        347      3478   | 3678  9       3568 |
| 1389    134789  6      | 5        2347     234789 | 1378  237     238  |
+------------------------+--------------------------+--------------------+
#3. Chain[4] : 5r3c3=5r7c3-5r7c8=(5-6)r6c8=6r1c8-6r1c4=6r3c5 :=> -5r3c5; 18 Singles; r79c8=23 :=> r9c9=8
#4. Chain[2] : Skyscraper(8C36) : r7c3=r6c3-r6c6=r8c6 :=> -8r7c4.r8c12;ste
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oaxen



Joined: 10 Jul 2006
Posts: 96

PostPosted: Fri Mar 01, 2013 6:17 pm    Post subject: Reply with quote

This was the hardes puzzles I ever met. I solved it, but canīt remember the step I took. something like van hay anyhow.
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Fri Mar 01, 2013 9:10 pm    Post subject: Reply with quote

oaxen wrote:
This was the hardes puzzles I ever met. I solved it, but canīt remember the step I took.


I hate when that happens. Smile
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keith



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

PostPosted: Fri Mar 01, 2013 10:32 pm    Post subject: Reply with quote

DonM wrote:
oaxen wrote:
This was the hardes puzzles I ever met. I solved it, but canīt remember the step I took.


I hate when that happens. Smile


oaxen,

I said:
Quote:
Ask, ye shall receive!
Very Happy

Keith
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Fri Mar 01, 2013 10:55 pm    Post subject: Reply with quote

Menneske Impossible 2 ssts ER=7.3
Code:
*-----------------------------------------------------------------------------*
 | 1239    1239    39      | 23469   8       12349   | 5       2346    7       |
 | 123589  6       7       | 2349    12345   12349   | 389     234     238     |
 | 4       23589   3589    | 7       2356    239     | 3689    1       2368    |
 |-------------------------+-------------------------+-------------------------|
 | 2356    235     1       | 2346    23467   2347    | 367     8       9       |
 | 3689    389     4       | 368     1367    5       | 2       367     136     |
 | 7       238     38      | 2368    9       1238    | 4       356     1356    |
 |-------------------------+-------------------------+-------------------------|
 | 13589   135789  3589    | 2389    237     6       | 1378    2357    4       |
 | 358     34578   2       | 1       347     3478    | 3678    9       3568    |
 | 1389    134789  6       | 5       2347    234789  | 1378    237     238     |
 *-----------------------------------------------------------------------------*

1. (5)r7c3=r3c3-r3c5=(5-1)r2c5=r5c5-r5c9=(1-5)r6c9=(5)r6c8 :=> -5r7c8 ->3 singles
Code:
*-----------------------------------------------------------------------------*
 | 1239    1239    39      |*23469   8       12349   | 5      *2346    7       |
 | 123589  6       7       | 2349    12345   12349   | 389     234     238     |
 | 4       23589   3589    | 7       2356    239     | 389     1       2368    |
 |-------------------------+-------------------------+-------------------------|
 | 2356    235     1       |G2346    23467   2347    | 37      8       9       |
 | 3689    389     4       |G368     137-6   5       | 2      *367    G136     |
 | 7       238     38      |*2368    9       1238    | 4       5      *136     |
 |-------------------------+-------------------------+-------------------------|
 | 13589   135789  3589    | 2389    237     6       | 1378    237     4       |
 | 38      3478    2       | 1       347     3478    | 6       9       5       |
 | 1389    134789  6       | 5       2347    234789  | 1378    237     238     |
 *-----------------------------------------------------------------------------*

2.(6)r45c4=[(6)BW:(6)r1c48,r5c8,r6c49]=(6)r5c9-r3c9=(6)r3c5 => -6r45c5 -> r3c5=6 => cascade of singles
-> np(89)r23c7 => r9c9=8 -> skyscraper(8)r5c4,r6c3,r7c34 => -8r6c6
stte

The core of step #2 of the solution is the BW or BrokenWing/Oddagon at (6)r1c48, r5c8, r6c49 (marked by *). This is a potential 5-sided loop of conjugate links of 6s which would be impossible if it existed by itelf. There are three 6s called 'Guardians' (marked by G above) at r4c45 and r5c9 that prevent that pattern. Thus, if guardian (6)r5c9 is not true then guardians (6)r45c4 must be true and vice-versa.

Of interest also: The BW pattern actually eliminates (6)r5c5 immediately because if it were true, it would eliminate all 3 guardians which can't happen. This is interesting because it is rare to find immediate BW eliminations in more complicated puzzles. BTW: Since the chain eliminates both 6s at r45c5 anyway, it isn't necessary to add this as a separate step.

(Keith, enjoyed these 2 puzzles-thanks!)
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oaxen



Joined: 10 Jul 2006
Posts: 96

PostPosted: Sat Mar 02, 2013 3:59 pm    Post subject: Reply with quote

Now I have recapitulated. Any of "ones" in block E gives correct five and six in block I. Next valuable bivalues are the "six" in block C. R1C8 leads to a complete puzzle. Very Happy
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arkietech



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

PostPosted: Fri Mar 08, 2013 12:31 pm    Post subject: Reply with quote

Code:
 *-----------------------------------------------------------------------------*
 | 1239    1239    39      | 23469   8       12349   | 5       2346    7       |
 | 123589  6       7       | 2349    12345   12349   | 389     234     238     |
 | 4       23589   3589    | 7       2356    239     | 3689    1       2368    |
 |-------------------------+-------------------------+-------------------------|
 | 2356    235     1       | 2346    23467   2347    | 367     8       9       |
 | 3689    389     4       | 368     1367    5       | 2       367     136     |
 | 7       238     38      | 2368    9       1238    | 4       356     1356    |
 |-------------------------+-------------------------+-------------------------|
 | 13589   135789  3589    | 2389    237     6       | 1378    2357    4       |
 | 358     34578   2       | 1       347     3478    | 3678    9       3568    |
 | 1389    134789  6       | 5       2347    234789  | 1378    237     238     |
 *-----------------------------------------------------------------------------*
net
5r3c5 5r7c3 5r6c8 6r6c9 6r1c8
5r3c5 6r1c4
contradiction -5r3c5
 
 *--------------------------------------------------------------------*
 | 1239   139    39     | 2349   8      12349  | 5      6      7      |
 | 12389  6      7      | 239    5      1239   | 89     4      23     |
 | 4      389    5      | 7      6      239    | 89     1      23     |
 |----------------------+----------------------+----------------------|
 | 6      5      1      | 24     247    247    | 3      8      9      |
 | 389    389    4      |f38     1      5      | 2      7      6      |
 | 7      2     *38     | 6      9      3-8    | 4      5      1      |
 |----------------------+----------------------+----------------------|
 | 5      13789 *389    |*289    237    6      | 17     23     4      |
 | 38     3478   2      | 1      347    478    | 6      9      5      |
 | 139    13479  6      | 5      2347   2479   | 17     23     8      |
 *--------------------------------------------------------------------*
Sashimi X-Wing
r67c34,fr5c4 => -8r6c6; ste
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