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many ways to crack this egg

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nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Nov 29, 2007 3:42 pm Post subject: many ways to crack this egg

In today's Vanheugen "fiendish" http://www.playr.co.uk/sudoku/index.php?class=5

Code:

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

it is almost embarrassing how quickly one gets to the point:

Code:

+--------------------------+--------------------------+--------------------------+
| 368 9 68 | 1 38 2 | 4 7 5 |
| 58 2 578 | 78 4 6 | 9 3 1 |
| 13 4 17 | 79 5 39 | 6 2 8 |
+--------------------------+--------------------------+--------------------------+
| 9 6 3 | 4 2 8 | 1 5 7 |
| 4 5 2 | 3 1 7 | 8 9 6 |
| 7 18 18 | 6 9 5 | 2 4 3 |
+--------------------------+--------------------------+--------------------------+
| 18 138 4 | 89 7 39 | 5 6 2 |
| 2 7 9 | 5 6 1 | 3 8 4 |
| 56 38 56 | 2 38 4 | 7 1 9 |
+--------------------------+--------------------------+--------------------------+

Plenty of ways to go from here:
a) coloring:
to remove 8 from r2c3 use this chain: -r2c4=r1c5-r9c5=r9c2-r6c2=r6c3-
(but still needs xy wing later on)

b) xy-wings:
pivot r1c3 removes 5 from the same cell r2c3 and from r9c1
pivot r2c1 removes 6 from r9c3 and r1c1

c) w-wings:
r6c2/r7c1 (by way of r6c3,r3c3,r3c4,r7c4)
r1c5/r9c2 (r2c4,r3c4,r3c6,r3c1,r7c1)

more?

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Thu Nov 29, 2007 4:40 pm Post subject:

how about xy-chain: r7c6=9, r7c4=8, r7c1=1, r3c1=3, r3c6<>3

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Nov 29, 2007 5:14 pm Post subject:

storm_norm wrote:

how about xy-chain:

True. I know, I know. Tons of xy-chains. Yuck.

No, I take it back. Sorry for the language. Just spent half an hour wading in chains.

They're great.

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Thu Nov 29, 2007 5:18 pm Post subject:

Isn't that a BUG+3 situation, too? r1c1=8 OR r2c3=8 OR r7c2=8 ? either way, r2c1<>8, the resulting BUG+1 solves it with r7c2=8 . Last edited by nataraj on Thu Nov 29, 2007 5:28 pm; edited 1 time in total

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Thu Nov 29, 2007 5:28 pm Post subject:

well I saw, 3,9 in column 6, and some other 3's and 9's so I went with it. yuck is right.

keith

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

Posted: Thu Nov 29, 2007 6:08 pm Post subject:

nataraj wrote:

Isn't that a BUG+3 situation, too?

r1c1=8 OR r2c3=8 OR r7c2=8 ?

either way, r2c1<>8, the resulting BUG+1 solves it with r7c2=8 .

As I see it, the BUG+3 means R1C3 <>8, which leads to a remote naked pair <38> which solves the puzzle.

Keith

re'born

Joined: 28 Oct 2007
Posts: 80

Posted: Thu Nov 29, 2007 8:30 pm Post subject: Re: many ways to crack this egg

nataraj wrote:

Plenty of ways to go from here:
a) coloring:
to remove 8 from r2c3 use this chain: -r2c4=r1c5-r9c5=r9c2-r6c2=r6c3-
(but still needs xy wing later on)

Start 3D-multicoloring from say r1c5. You will only need two colors and you quickly find a wealth of deductions.

ravel

Joined: 21 Apr 2006
Posts: 536

Posted: Thu Nov 29, 2007 10:14 pm Post subject:

Code:

+--------------------------+--------------------------+--------------------------+
|#368 9 #68 | 1 38 2 | 4 7 5 |
|#58 2 #578 | 78 4 6 | 9 3 1 |
| 13 4 17 | 79 5 39 | 6 2 8 |
+--------------------------+--------------------------+--------------------------+
| 9 6 3 | 4 2 8 | 1 5 7 |
| 4 5 2 | 3 1 7 | 8 9 6 |
| 7 18 18 | 6 9 5 | 2 4 3 |
+--------------------------+--------------------------+--------------------------+
| 18 138 4 | 89 7 39 | 5 6 2 |
| 2 7 9 | 5 6 1 | 3 8 4 |
|#56 38 #56 | 2 38 4 | 7 1 9 |
+--------------------------+--------------------------+--------------------------+

Alternatively to the BUG+3 you can use this deadly pattern (68,58,56). Because of the strong links for 6 in row 1 and 5 in r2 it eliminates 8 from r1c3 and r2c1, 6 from r1c1 and r9c3, and 5 from r2c3 and r9c1.
The BUG+1 finishes it then.

re'born

Joined: 28 Oct 2007
Posts: 80

Posted: Fri Nov 30, 2007 9:23 am Post subject:

ravel wrote:

Code:

I'm not satisfied with the deadly pattern. The rule of thumb ronk taught me for deciding whether something is a deadly pattern is that each candidate in the pattern should occur twice in every row, column and block. In this case 8 occurs 4 times in the pattern in block 1 and so I would think it would not be a deadly pattern. Thoughts?

keith

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

Posted: Fri Nov 30, 2007 11:36 am Post subject:

re'born wrote:

ravel wrote:

Code:

Well, the pattern that ravel is avoiding is this:

Code:

+------------+
| 68 . 68 |
| 58 . 58 |
| . . . |
+------------+
| . . . |
| . . . |
| . . . |
+------------+
| . . . |
| . . . |
| 56 . 56 |
+------------+

which is clearly not a valid pattern. But, I think ravel's logic is correct. He is avoiding an invalid solution (pattern), albeit not one that has multiple solutions The more usual deadly pattern would be like this:

Code:

+------------+
| 68 . 68 |
| . . . |
| . . . |
+------------+
| . . . |
| 58 . 58 |
| . . . |
+------------+
| . . . |
| . . . |
| 56 . 56 |
+------------+

Keith

ravel

Joined: 21 Apr 2006
Posts: 536

Posted: Fri Nov 30, 2007 11:41 am Post subject:

re'born wrote:

Ah, thanks, of course you are right. This pattern in one box definitely is impossible.

Code:

+--------------------------+
| 68 . 68 |
| 58 . 58 |
-----

I deleted the other post, where i made the same mistake, but the eliminations were not correct.

PS:
This is a deadly pattern with 3 digits in a box:

Code:

| abc abc abc |
| . . . |
| . . . |
--------------
| abc abc abc |
| . . . |
| . . . |

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