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keith

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

Posted: Sat Aug 28, 2010 7:02 pm Post subject: Free Press Aug 27, 2010

Not yet started ...

Code:

Puzzle: FP082710
+-------+-------+-------+
| 3 4 . | . 7 . | 2 8 . |
| 5 . . | 8 . 6 | . . 9 |
| . . . | . . . | 7 . . |
+-------+-------+-------+
| . . . | 3 . 4 | . 1 . |
| . . . | . 9 . | . . . |
| . 6 . | . . 2 | . . . |
+-------+-------+-------+
| . . 7 | . . . | . . . |
| 8 . . | 9 . 1 | . . 4 |
| . 5 9 | . 6 . | . 3 2 |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Keith

keith

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

Posted: Sat Aug 28, 2010 8:31 pm Post subject:

After basics:

Code:

+-------------------+-------------------+-------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 123 6 | 13 4 9 |
| 1269 1289 1268 | 1245 12345 35 | 7 56 1356 |
+-------------------+-------------------+-------------------+
| 279 289 258 | 3 58 4 | 5689 1 5678 |
| 17 138 13458 | 6 9 578 | 3458 2 3578 |
| 79 6 3458 | 157 158 2 | 34589 59 3578 |
+-------------------+-------------------+-------------------+
| 1246 123 7 | 245 23458 358 | 15689 569 1568 |
| 8 23 236 | 9 235 1 | 56 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+-------------------+-------------------+-------------------+

After two wings, I am more or less stuck.

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Aug 28, 2010 9:55 pm Post subject:

After an X-Wing and 2x M-Wings, my solver resorted to a chain to get past the bottleneck.

While examining a network contradiction, I managed to construct a single-stepper:

Code:

+-----------------------------------------------------------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 123 6 | 13 4 9 |
| 1269 1289 1268 | 1245 12345 35 | 7 56 1356 |
|-----------------------+-----------------------+-----------------------|
| 279 289 258 | 3 58 4 | 5689 1 5678 |
| 17 138 13458 | 6 9 578 | 3458 2 3578 |
| 79 6 3458 | 157 158 2 | 34589 59 3578 |
|-----------------------+-----------------------+-----------------------|
| 1246 123 7 | 245 23458 358 | 15689 569 1568 |
| 8 23 236 | 9 235 1 | 56 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+-----------------------------------------------------------------------+
# 105 eliminations remain

Quote:

(5)r8c5 = (5-6)r8c7 = (6)r8c3 - ALS(3=1268=5)r81234c3 => r4c5<>5

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Aug 29, 2010 11:12 am Post subject:

having some fun with AHS, found two in this solution path.

after this x-wing

Code:

+---------------------+------------------+----------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 123 6 | 13 4 9 |
| 129(6) 1289 128-6 | 1245 12345 35 | 7 5(6) 135-6 |
+---------------------+------------------+----------------------+
| 279 289 258 | 3 58 4 | 5689 1 5678 |
| 17 138 13458 | 6 9 578 | 3458 2 3578 |
| 79 6 3458 | 157 158 2 | 34589 59 3578 |
+---------------------+------------------+----------------------+
| 124(6) 123 7 | 245 23458 358 | 1589-6 59(6) 158-6 |
| 8 23 236 | 9 235 1 | 56 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+---------------------+------------------+----------------------+

#1...x-wing on 6; r3c39 and r7c79 all not 6

--------------

Code:

+---------------------+----------------------+-------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 123 6 | 13 4 9 |
| 1269 1289 128 | 1245 12345 35 | 7 56 135 |
+---------------------+----------------------+-------------------+
| 27(9) 28(9) 258 | 3 8(5) 4 | 58(69) 1 5678 |
| 17 138 13458 | 6 9 -8(57) | 3458 2 3578 |
| (79) 6 3458 | 1(57) 18(5) 2 | 34589 59 3578 |
+---------------------+----------------------+-------------------+
| 1246 123 7 | 245 23458 358 | 1589 569 158 |
| 8 23 236 | 9 23(5) 1 | (56) 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+---------------------+----------------------+-------------------+

#2...(57)r56c13 = (5)r46c5 - (5)r8c5 = (5-6)r8c7 = (6-9)r4c7 = (9)r4c12 - (9=7)r6c1 - (7)r6c4 = (7)r5c6; r5c6 <> 8

----------------------

Code:

+-------------------+-------------------+------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 12-3 6 | (13) 4 9 |
| 1269 1289 128 | 1245 12345 (35) | 7 56 15-3 |
+-------------------+-------------------+------------------+
| 279 289 258 | 3 58 4 | 5689 1 5678 |
| 17 138 13458 | 6 9 (57) | 3458 2 3578 |
| 79 6 3458 | 157 158 2 | 34589 59 3578 |
+-------------------+-------------------+------------------+
| 1246 123 7 | 245 2345 358 | 1589 569 158 |
| 8 23 236 | 9 235 1 | 56 7 4 |
| 14 5 9 | 47 6 (78) | (18) 3 2 |
+-------------------+-------------------+------------------+

#3... (3=5)r3c6 - (5=7)r5c6 - (7=8)r9c6 - (8=1)r9c7 - (1=3)r2c7; r2c5 and r3c9 <> 3

--------------

Code:

+-------------------+------------------+----------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 12 6 | 3 4 9 |
| 1269 1289 128 | 1245 12345 35 | 7 56 15 |
+-------------------+------------------+----------------------+
| 279 289 258 | 3 58 4 | 589(6) 1 5-8(67) |
| 17 138 13458 | 6 9 57 | 458 2 5-8(37) |
| 79 6 3458 | 157 158 2 | 4589 59 5-8(37) |
+-------------------+------------------+----------------------+
| 1246 123 7 | 245 2345 358 | 1589 569 (58) |
| 8 23 236 | 9 235 1 | (56) 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+-------------------+------------------+----------------------+

#4... (37)r56c9 = (7-6)r4c9 = (6)r4c7 - (6=5)r8c7 - (5=8)r7c9; r456c9 <> 8

the easier chain to see is: (6)r4c9 = (6)r4c7 - (6=5)r8c7 - (5=8)r7c9 which gets rid of one 8 in r4c9.
but understanding that the 7 in r4c9 is also strongly linked to the almost hidden set of {3,7} in r56c9 will get the other two 8's eliminated as well since they occupy the cells of the AHS.

------------------

Code:

+-----------------+--------------+----------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 12 6 | 3 4 9 |
| 269 289 128 | 24 34 35 | 7 56 15 |
+-----------------+--------------+----------------+
| 279 29-8 25-8 | 3 (58) 4 | 5689 1 567 |
| 1 (38) 3458 | 6 9 7 | 458 2 35 |
| 79 6 3458 | 15 158 2 | 4589 59 357 |
+-----------------+--------------+----------------+
| 26 1 7 | 24 34 35 | 59 569 8 |
| 8 (23) 236 | 9 (25) 1 | 56 7 4 |
| 4 5 9 | 7 6 8 | 1 3 2 |
+-----------------+--------------+----------------+

#5... (8=5)r4c5 - (5=2)r8c5 - (2=3)r8c2 - (3=8)r5c2; r4c34 <> 8

then a naked triple, then its easy basics from there.

peterj

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

Posted: Sun Aug 29, 2010 3:25 pm Post subject:

Seemed to be lots of m-wing like patterns, I sort of stuck two together for this elimination

Code:

+---------------------+-------------------+-------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 123 6 | 13 4 9 |
| 12(69) 128(9) 1268 | 1245 12345 35 | 7 56 1356 |
+---------------------+-------------------+-------------------+
| 2(7)9 28-9 258 | 3 58 4 | 5(6)89 1 5(67)8 |
| 17 138 13458 | 6 9 578 | 3458 2 3578 |
| (79) 6 3458 | 157 158 2 | 34589 59 3578 |
+---------------------+-------------------+-------------------+
| 124(6) 123 7 | 245 23458 358 | 15689 569 1568 |
| 8 23 23(6) | 9 235 1 | 5(6) 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+---------------------+-------------------+-------------------+

(9=7)r6c1 - r4c1=(7-6)r4c9=r4c7 - r8c7=r8c3 - r7c1=(6-9)r3c1=r3c2 ; r4c2<>9

Then...

xy-wing(58-2) r4c5 ; r8c2<>2

finishes it off..

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Aug 29, 2010 6:03 pm Post subject:

After the X-Wing, HoDoKu performs:

Code:

Sue de Coq: r4c23 - {2589} (r4c5 - {58}, r456c1 - {1279}) => r5c23<>1, r4c79<>58
+-----------------------------------------------------------------------+
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 123 6 | 13 4 9 |
| 1269 1289 128 | 1245 12345 35 | 7 56 135 |
|-----------------------+-----------------------+-----------------------|
| 279 289 258 | 3 58 4 | 5689 1 5678 |
| 17 138 13458 | 6 9 578 | 3458 2 3578 |
| 79 6 3458 | 157 158 2 | 34589 59 3578 |
|-----------------------+-----------------------+-----------------------|
| 1246 123 7 | 245 23458 358 | 1589 569 158 |
| 8 23 236 | 9 235 1 | 56 7 4 |
| 14 5 9 | 47 6 78 | 18 3 2 |
+-----------------------------------------------------------------------+
# 101 eliminations remain

Since I don't know this technique, I studied the cells highlighted for the technique.

What I discovered is that I can get the same results by alternating r4c1=2 and r4c1<>2.

Code:

band 2 after r4c1=2 => r5c23<>1, r4c79<>58
|-------------------+-------------------+-------------------|
| 2 9 58 | 3 58 4 | 6 1 7 |
| 1 38 3458 | 6 9 7 | 458 2 35 |
| 7 6 3458 | 15 158 2 | 489 59 35 |
|-------------------+-------------------+-------------------|

band 2 after r4c1<>2 => r5c23<>1, r4c79<>58
|----------------------+----------------------+----------------------|
| 79 28 258 | 3 58 4 | 69 1 67 |
| 1 38 3458 | 6 9 578 | 3458 2 3578 |
| 79 6 3458 | 157 158 2 | 34589 59 3578 |
|----------------------+----------------------+----------------------|

A Kite and Skyscraper follow to finish off the puzzle.

tlanglet

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

Posted: Mon Aug 30, 2010 3:20 pm Post subject:

A solution using three "almost" steps.......

1. x-wing 6 r37c18; r3c39,r7c79<>6

2. ANP(79=2)r46c1-r4c23*=ls(58)r4c35-(28=9)r4c2*-(9=7)r6c1; r5c1<>7

At this point the code is:

Code:

*-----------------------------------------------------------*
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 12 6 | 3 4 9 |
| 269 289 128 | 24 34 35 | 7 56 15 |
|-------------------+-------------------+-------------------|
| 279 289 258 | 3 58 4 | 5689 1 5678 |
| 1 38 3458 | 6 9 7 | 458 2 358 |
| 79 6 3458 | 15 158 2 | 4589 59 3578 |
|-------------------+-------------------+-------------------|
| 26 1 7 | 24 34 35 | 589 569 58 |
| 8 23 236 | 9 25 1 | 56 7 4 |
| 4 5 9 | 7 6 8 | 1 3 2 |
*-----------------------------------------------------------*

3. AXY-wing 56-8 with vertex (56)r8c7, pincers (68)r4c7 & (58)r7c9 with fin (59)r4c7
If fin is true: r456c9,r7c7<>8
If fin is true: ls(59)r4c7|r6c8-(59=48)r56c7; r456c9,r7c7<>8

Which brings us to:

Code:

*-----------------------------------------------------------*
| 3 4 16 | 15 7 9 | 2 8 156 |
| 5 7 12 | 8 12 6 | 3 4 9 |
| 269 289 128 | 24 34 35 | 7 56 15 |
|-------------------+-------------------+-------------------|
| 279 289 258 | 3 58 4 | 5689 1 567 |
| 1 38 3458 | 6 9 7 | 458 2 35 |
| 79 6 3458 | 15 158 2 | 4589 59 357 |
|-------------------+-------------------+-------------------|
| 26 1 7 | 24 34 35 | 59 569 8 |
| 8 23 236 | 9 25 1 | 56 7 4 |
| 4 5 9 | 7 6 8 | 1 3 2 |
*-----------------------------------------------------------*

4.AHT(238=9)r458c2-(9=7)r6c1-r6c9=(7-6)r4c9=r1c9-(6=1=2=8)r12*3c3-(28)r3c2; r3c2<>28=9

5. Coloring 5 or AIC found by extending vertex of potential xy-wing: (9=5)r6c8-r6c4=r1c4-(5=6)r1c9-(6=7)r4c9-(7=9)r4c1; r6c1<>9

Ted

tlanglet

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

Posted: Mon Aug 30, 2010 3:23 pm Post subject:

peterj wrote:

Seemed to be lots of m-wing like patterns, I sort of stuck two together for this elimination

Code:

(9=7)r6c1 - r4c1=(7-6)r4c9=r4c7 - r8c7=r8c3 - r7c1=(6-9)r3c1=r3c2 ; r4c2<>9

Then...

xy-wing(58-2) r4c5 ; r8c2<>2

finishes it off..

Great move..........

Ted

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