UR Pattern(s) -- Analysis

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UR Pattern(s) -- Analysis

Postby daj95376 » Mon Jan 19, 2009 4:34 am

Code: Select all
 Set J Puzzle #2
 +-----------------------+
 | 5 . 9 | . 4 . | . 2 . |
 | . 7 . | 6 . . | 9 . . |
 | 2 . . | 9 . 7 | . 4 5 |
 |-------+-------+-------|
 | . 1 2 | . 8 . | 4 . . |
 | 8 . . | 4 9 . | . . . |
 | . . 7 | . . 2 | . . . |
 |-------+-------+-------|
 | . 5 . | 1 . . | 2 . . |
 | 4 . 8 | . . . | . 1 . |
 | . . 1 | . . . | . . . |
 +-----------------------+

 after: basics, Skyscraper on <1>, basics
 note: X-Wing pattern on <4>
 *-----------------------------------------------------------*
 | 5     6     9     | 38    4     38    | 1     2     7     |
 | 1     7     4     | 6     2     5     | 9     38    38    |
 | 2     8     3     | 9     1     7     | 6     4     5     |
 |-------------------+-------------------+-------------------|
 | 69    1     2     | 7     8     36    | 4     5     39    |
 | 8     3     5     | 4     9     1     | 7     6     2     |
 | 69    4     7     | 35    56    2     | 38    389   1     |
 |-------------------+-------------------+-------------------|
 | 7     5     6     | 1     3    *489   | 2     89   *489   |
 | 4     29    8     | 25    7     69    | 35    1     369   |
 | 3     29    1     | 258   56   *4689  | 58    7    *4689  |
 *-----------------------------------------------------------*

Although a couple of XY-Wings will finish the puzzle, I'm more interested in a pair of UR patterns in [r79c69].

Code: Select all
[r7c8]=8 + <49> UR4 [r79c69] => [r9c9]<>89
[r7c8]=9 + <48> UR4 [r79c69] => [r9c9]<>89

Is there a better/simpler way to get these eliminations? If not, does this approach have a name?

Is there a reasonable way to get [r7c9]<>8 or [r9c6]<>8?
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Re: UR Pattern(s) -- Analysis

Postby hobiwan » Mon Jan 19, 2009 5:58 am

daj95376 wrote:Is there a reasonable way to get [r7c9]<>8 or [r9c6]<>8?

Since "reasonable" is a relativ term I let you decide yourself:D

[r7c9]<>8:

XY-Chain: 8 r9c7 -5- r9c5 -6- r6c5 -5- r6c4 -3- r4c6 -6- r4c1 -9- r4c9 -3- r2c9 => r79c9<>8
AIC 8- r7c8 -9- r6c8 =9= r6c1 =6= r6c5 =5= r9c5 -5- r9c7 -8=> r79c9<>8
ALS XY-Wing: A=r7c8 - {89}, B=r9c57 - {568}, C=r6c4578 - {35689}, X,Y=6,9, Z=8 => r79c9<>8

[r9c6]<>8 would be a bad idea since r9c6=8 in the solution.

As to your step it looks like a Forcing Chain Verity to me.
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Re: UR Pattern(s) -- Analysis

Postby eleven » Mon Jan 19, 2009 8:42 am

daj95376 wrote:Is there a better/simpler way to get these eliminations?
Your way is nice enough:) I dont remember to have seen this pattern before (and never looked for it).
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Re: UR Pattern(s) -- Analysis

Postby daj95376 » Mon Jan 19, 2009 11:53 am

hobiwan wrote:As to your step it looks like a Forcing Chain Verity to me.

I agree. That's partly why I asked for an alternate way to get the eliminations. I was hoping that someone would turn it into a loop with two UR conditions. Sorry about the oversight in cell [r9c6].

eleven wrote:Your way is nice enough. I don't remember having seen this pattern before (and never looked for it).

Yes, it was a surprise to me. I'm accustomed to having a UR search fail because of the UR candidates being present as a pair in a neighboring cell. While looking for such a condition, I ran across this strange example.
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Postby Steve K » Mon Jan 19, 2009 6:28 pm

One can eliminate both (89) from r9c9 independently, and upon inspection:
First note (xwing4)r79c69:
(AUR48)r79c69 => (8)r7c8=(8)r9c47 => r9c9<>8
(AUR49)r79c69 => (9)r7c8=(9)r9c2 => r9c9<>9
Although combining the two into one larger chain seems a bit superfluous, using internal pauses it easily done using (8-9)r7c8.
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Re: UR Pattern(s) -- Analysis

Postby aran » Tue Jan 20, 2009 5:37 am

daj95376 wrote:
Code: Select all
 
 *-----------------------------------------------------------*
 | 5     6     9     | 38    4     38    | 1     2     7     |
 | 1     7     4     | 6     2     5     | 9     38    38    |
 | 2     8     3     | 9     1     7     | 6     4     5     |
 |-------------------+-------------------+-------------------|
 | 69    1     2     | 7     8     36    | 4     5     39    |
 | 8     3     5     | 4     9     1     | 7     6     2     |
 | 69    4     7     | 35    56    2     | 38    389   1     |
 |-------------------+-------------------+-------------------|
 | 7     5     6     | 1     3    *489   | 2     89   *489   |
 | 4     29    8     | 25    7     69    | 35    1     369   |
 | 3     29    1     | 258   56   *4689  | 58    7    *4689  |
 *-----------------------------------------------------------*


Another longer way...
389r248c9=6r8c9-(6=9)r8c6-(9=2)r8c2-(2=5)r8c4-(5=6)r9c5-(69=48)r79c6-UR(48)r79c69=9r79c9-(9=8)r7c8 (=> <8>r79c9) -(89=4)r7c6-4r9c6=4r9c9 : <9>r9c9

(edited to correct inversion rows/columns first node)
Last edited by aran on Tue Jan 20, 2009 6:01 pm, edited 1 time in total.
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Postby daj95376 » Tue Jan 20, 2009 7:01 am

Thanks to everyone for your replies. Now, I need to study them closely.
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Postby daj95376 » Sat Jan 24, 2009 4:33 pm

I'm still working with URs on a very basic level.

Code: Select all
 +-----------------------+
 | 1 4 . | . . . | 8 6 . |
 | 9 6 . | 7 . . | . . 1 |
 | . . 8 | 1 . . | . . . |
 |-------+-------+-------|
 | . 1 7 | 8 3 . | 4 9 . |
 | . . . | 4 . . | . 1 . |
 | . . . | . . . | . . . |
 |-------+-------+-------|
 | 8 . . | 6 . . | . 7 . |
 | 4 . . | 3 8 . | 2 . . |
 | . 5 . | . . . | . . 6 |
 +-----------------------+

Code: Select all
 after Singles, Naked Pairs, and a Remote Pair
 +--------------------------------------------------------------+
 |  1     4     5     |  29    29    3     |  8     6     7     |
 |  9     6     23    |  7     4     8     |  5     23    1     |
 |  7     23    8     |  1     56    56    |  9     4     23    |
 |--------------------+--------------------+--------------------|
 |  256   1     7     |  8     3     26    |  4     9     25    |
 |  356-2 2389  239   |  4     269   279-6 |  67    1     2358  |
 |  236   89    4     |  5     1     279-6 |  67    23    238   |
 |--------------------+--------------------+--------------------|
 |  8     239   129-3 |  6     259   259   |  13    7     4     |
 |  4     7     6     |  3     8     1     |  2     5     9     |
 |  23    5     129-3 |  29    7     4     |  13    8     6     |
 +--------------------------------------------------------------+
 # 55 eliminations remain

 25 UR  [r45c19]  =>  [r5 c1]<>2
 67 UR4 [r56c67]  =>  [r56c6]<>6
 13 UR4 [r79c47]  =>  [r79c3]<>3

Are there any more UR eliminations in this PM? TIA!!!
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Postby aran » Sat Jan 24, 2009 9:03 pm

daj95376 wrote:I'm still working with URs on a very basic level.

Code: Select all
 +-----------------------+
 | 1 4 . | . . . | 8 6 . |
 | 9 6 . | 7 . . | . . 1 |
 | . . 8 | 1 . . | . . . |
 |-------+-------+-------|
 | . 1 7 | 8 3 . | 4 9 . |
 | . . . | 4 . . | . 1 . |
 | . . . | . . . | . . . |
 |-------+-------+-------|
 | 8 . . | 6 . . | . 7 . |
 | 4 . . | 3 8 . | 2 . . |
 | . 5 . | . . . | . . 6 |
 +-----------------------+

Code: Select all
 after Singles, Naked Pairs, and a Remote Pair
 +--------------------------------------------------------------+
 |  1     4     5     |  29    29    3     |  8     6     7     |
 |  9     6     23    |  7     4     8     |  5     23    1     |
 |  7     23    8     |  1     56    56    |  9     4     23    |
 |--------------------+--------------------+--------------------|
 |  256   1     7     |  8     3     26    |  4     9     25    |
 |  356-2 2389  239   |  4     269   279-6 |  67    1     2358  |
 |  236   89    4     |  5     1     279-6 |  67    23    238   |
 |--------------------+--------------------+--------------------|
 |  8     239   129-3 |  6     259   259   |  13    7     4     |
 |  4     7     6     |  3     8     1     |  2     5     9     |
 |  23    5     129-3 |  29    7     4     |  13    8     6     |
 +--------------------------------------------------------------+
 # 55 eliminations remain

 25 UR  [r45c19]  =>  [r5 c1]<>2
 67 UR4 [r56c67]  =>  [r56c6]<>6
 13 UR4 [r79c47]  =>  [r79c3]<>3

Are there any more UR eliminations in this PM? TIA!!!

<2>r5c2 using UR29r57c23 and taking advantage of the elims you have already found :
38r5c2-2r5c2 : <2>r5c2
3r7c2-(3=2)r3c2 : <2>r5c2
1r7c3-1r9c3=(29)r9c34-(2=3)r9c1-(3=256)r456c1 : <2>r5c2
3r5c3-(3=2)r2c3-(2=19)r79c3-9r7c2=23r37c2 : <2>r5c2
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Postby daj95376 » Sun Jan 25, 2009 2:58 am

aran wrote:
Code: Select all
 after Singles, Naked Pairs, and a Remote Pair
 +--------------------------------------------------------------+
 |  1     4     5     |  29    29    3     |  8     6     7     |
 |  9     6     23    |  7     4     8     |  5     23    1     |
 |  7     23    8     |  1     56    56    |  9     4     23    |
 |--------------------+--------------------+--------------------|
 |  256   1     7     |  8     3     26    |  4     9     25    |
 |  356-2 2389  239   |  4     269   279-6 |  67    1     2358  |
 |  236   89    4     |  5     1     279-6 |  67    23    238   |
 |--------------------+--------------------+--------------------|
 |  8     239   129-3 |  6     259   259   |  13    7     4     |
 |  4     7     6     |  3     8     1     |  2     5     9     |
 |  23    5     129-3 |  29    7     4     |  13    8     6     |
 +--------------------------------------------------------------+
 # 55 eliminations remain

<2>r5c2 using UR29r57c23

I need for you to explain your elimination.

When I set [r5c2]=2, then I get [r2c3]=[r9c1]=2 ... and there is no way the 29 pattern can be completed with [r7c3]=2.
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Postby aran » Sun Jan 25, 2009 4:15 am

daj95376 wrote:
aran wrote:
Code: Select all
 after Singles, Naked Pairs, and a Remote Pair
 +--------------------------------------------------------------+
 |  1     4     5     |  29    29    3     |  8     6     7     |
 |  9     6     23    |  7     4     8     |  5     23    1     |
 |  7     23    8     |  1     56    56    |  9     4     23    |
 |--------------------+--------------------+--------------------|
 |  256   1     7     |  8     3     26    |  4     9     25    |
 |  356-2 2389  239   |  4     269   279-6 |  67    1     2358  |
 |  236   89    4     |  5     1     279-6 |  67    23    238   |
 |--------------------+--------------------+--------------------|
 |  8     239   129-3 |  6     259   259   |  13    7     4     |
 |  4     7     6     |  3     8     1     |  2     5     9     |
 |  23    5     129-3 |  29    7     4     |  13    8     6     |
 +--------------------------------------------------------------+
 # 55 eliminations remain

<2>r5c2 using UR29r57c23

I need for you to explain your elimination.

When I set [r5c2]=2, then I get [r2c3]=[r9c1]=2 ... and there is no way the 29 pattern can be completed with [r7c3]=2.

You could look at it like : starting a discontinuous loop with [r5c2]=2 :
2r5c2-(2=3)r3c2-(3=2)r2c3-(2=19)r79c3-9r7c2=23r37c2-2r5c2 : =><2>r5c2
(ie if it's true, it's false)
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