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Stuck Again

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Stuck Again

Postby Tapestry » Sun Dec 21, 2008 8:44 am

It's probably something really simple, but I can't see it. Here's the original:

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

Here's how far I got (not far):

.---------------.---------------.-----------------.
| 679 4 379 | 36 2 369 | 1 5 8 |
| 8 25 259 | 1 4 7 | 29 3 6 |
| 269 236 1 | 5 8 369 | 29 7 4 |
:---------------+---------------+-----------------:
| 3 17 479 | 2 6 8 | 5 14 79 |
| 279 257 2579 | 4 3 1 | 6 8 79 |
| 46 168 48 | 7 9 5 | 3 14 2 |
:---------------+---------------+-----------------:
| 1 238 238 | 68 7 26 | 4 9 5 |
| 5 278 2478 | 9 1 24 | 78 6 3 |
| 47 9 6 | 38 5 34 | 78 2 1 |
'---------------'---------------'-----------------'

Thanks!
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Postby Luke » Sun Dec 21, 2008 9:36 am

Try xy-chains when there are a good number of bivalue cells like this.
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Re: Stuck Again

Postby aran » Sun Dec 21, 2008 12:56 pm

Tapestry wrote:It's probably something really simple, but I can't see it. Here's the original:

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

Here's how far I got (not far):

.---------------.---------------.-----------------.
| 679 4 379 | 36 2 369 | 1 5 8 |
| 8 25 259 | 1 4 7 | 29 3 6 |
| 269 236 1 | 5 8 369 | 29 7 4 |
:---------------+---------------+-----------------:
| 3 17 479 | 2 6 8 | 5 14 79 |
| 279 257 2579 | 4 3 1 | 6 8 79 |
| 46 168 48 | 7 9 5 | 3 14 2 |
:---------------+---------------+-----------------:
| 1 238 238 | 68 7 26 | 4 9 5 |
| 5 278 2478 | 9 1 24 | 78 6 3 |
| 47 9 6 | 38 5 34 | 78 2 1 |
'---------------'---------------'-----------------'

Thanks!

A way home maybe not the shortest :
1. hidden triple : 257r258c2=8r8c2-8r8c7=8r9c7-(8=3)r9c4-(3=4)r9c6-4r9c1=4r6c1-(4=1)r6c8-1r4c8=1r4c2 => <7>r4c2 : placements : 1 r4c2,r6c8 ; 4 r4c8+eliminations arising.
2. AUR (79) : r45c39 => <79> r5c3
3. AUR (25) : r25c23 =>
(i) 7r5c2=9r2c3=7r4c3 => <7>r5c1
(ii) 9r2c3=7r5c2=9r4c3 => <9>r1c3
4. discontinuous nice loop : (7=3)r1c3-(3=6)r1c4-(6=8)r7c4-8r9c4=(8-7)r9c7=7r9c1-7r1c1=7r1c3 => r1c3=7
Singles from there
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Re: Stuck Again

Postby eleven » Mon Dec 22, 2008 12:25 am

Tapestry wrote:It's probably something really simple, but I can't see it.

Tapestry, i dont know, how you could place the two 6's and the 8, but you missed a unique rectangle, which immediately solves it:
Code: Select all
.-------.-------.-------.
| . 4 . | . . . | 1 5 . |
| 8 . . | . . 7 | . . 6 |
| . . 1 | . 8 . | . . 4 |
:-------+-------+-------:
| 3 . . | 2 6 . | . . . |
| . . . | 4 . 1 | . . . |
| . . . | . 9 5 | . . 2 |
:-------+-------+-------:
| 1 . . | . 7 . | 4 . . |
| 5 . . | 9 1 . | . . 3 |
| . 9 6 | . . . |. 2 .  |
'-------'-------'-------'
.-------------------.-------------------.-------------------.
| 679   4     379   | 36    2     369   | 1     5     8     |
| 8     25    259   | 1     4     7     | 29    3     6     |
| 269   236   1     | 5     8     369   | 29    7     4     |
:-------------------+-------------------+-------------------:
| 3     17    479   | 2     6     8     | 5     14    79    |
| 279   257   2579  | 4     3     1     |#6    #8     79    |
| 46    168   48    | 7     9     5     | 3     14    2     |
:-------------------+-------------------+-------------------:
| 1     238   238   | 68    7     26    | 4     9     5     |
| 5     278   2478  | 9     1     24    |#78   #6     3     |
| 47    9     6     | 38    5     34    | 78    2     1     |
'-------------------'-------------------'-------------------'

Since none of the marked cells has a given, r8c7 cannot be 8.
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Postby storm_norm » Mon Dec 22, 2008 8:14 pm

Code: Select all
.------------------.------------------.------------------.
| 679   4     379  | 36    2     369  | 1     5     8    |
| 8     25    259  | 1     4     7    | 29    3     6    |
| 269   236   1    | 5     8     369  | 29    7     4    |
:------------------+------------------+------------------:
| 3     17    479  | 2     6     8    | 5     14    79   |
| 279   257   2579 | 4     3     1    | 6     8     79   |
| 46    168   48   | 7     9     5    | 3     14    2    |
:------------------+------------------+------------------:
| 1     238   238  | 68    7     26   | 4     9     5    |
| 5     278   2478 | 9     1     24   | 78    6     3    |
| 47    9     6    | 38    5     34   | 78    2     1    |
'------------------'------------------'------------------'

1. (6=4)r6c1 - (4)r9c1 = (4)r9c6 - (4=2)r8c6 - (2=6)r7c6 - (6)r7c4 = (6)r1c4; r1c1 <> 1
2. xy-chain... (9=7)r1c1 - (7=4)r9c1 - (4=3)r9c6 - (3=9)r3c6; r1c6 <> 9
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Postby StrmCkr » Mon Dec 22, 2008 8:45 pm

eleven wrote:Since none of the marked cells has a given, r8c7 cannot be 8

im guessing your going on the notation of a ur 1.1 correct?
Some do, some teach, the rest look it up.
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Postby eleven » Tue Dec 23, 2008 1:17 am

Yes, after the placement of 8 in r5c8 and the 6's in r5c7 and r8c8 its a UR1.1. That means, that the 8 in r8c7 can be eliminated without a knowledge, that the puzzle is unique.
But i still dont see an easy way to make those placements without using this UR 68.
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Postby Draco » Tue Dec 23, 2008 4:40 am

From Tapestry's PMs there is also a quick forcing chain that cracks the puzzle to singles:
Code: Select all
679 4   379  | 36 2 369 | 1  5  8
8   25  259  | 1  4 7   | 29 3  6
269 236 1    | 5  8 369 | 29 7  4
-------------+----------+---------
3   17  479  | 2  6 8   | 5  14 79
279 257 2579 | 4  3 1   | 6  8  79
46  168 48   | 7  9 5   | 3  14 2
-------------+----------+---------
1   238 238  | 68 7 26  | 4  9  5
5   278 2478 | 9  1 24  | 78 6  3
47  9   6    | 38 5 34  | 78 2  1

r3c2=3 r6c2=6 r6c1=4 +  r7c2=3 r3c6=3 r9c6=4 ==> r9c1<>4

And in looking at the original puzzle and eleven's solution, if you clear singles, patterns and locked sets from the get-go, you'll find a UR type 1 using the same cells eleven identified:
Code: Select all
679 4   379  | 36 2 369 | 1    5  8
8   25  259  | 1  4 7   | 29   3  6
269 236 1    | 5  8 369 | 29   7  4
-------------+----------+-----------
3   17  479  | 2  6 8   | 5   14  79
279 257 2579 | 4  3 1   |#68  #68 79
46  168 48   | 7  9 5   | 3   14  2
-------------+----------+-----------
1   238 238  | 68 7 26  | 4    9  5
5   278 2478 | 9  1 24  |#678 #68 3
47  9   6    | 38 5 34  | 78   2  1

Cheers...

- drac
[edit: added original PMs ease of viewing]
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