Double Implication Chain???

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Double Implication Chain???

Postby Jasper32 » Thu Nov 20, 2008 5:02 am

Code: Select all

I worked this puzzle to this point. In a "solver" it stated that by using either the (4) or the (7) in r2c2, the (3) in r7c4 could be eliminated. I can see how using the (4) in r2c2 can force r2c4 to be (3) hence the (3) in r7c4 can be eliminated. But I cannot figure out how using the (7) in r2c2 can force this elimination in r7c4. Is this a Forcing Chain or a Double Implication Chain or are the terms synonymous.

Any help is truly appreciated.
 
 *-----------------------------------------------------------*
 | 37    5     378   | 29    6     279   | 4     89    1     |
 | 1     47    9     | 34    347   8     | 5     6     2     |
 | 2     48    6     | 459   1     459   | 7     89    3     |
 |-------------------+-------------------+-------------------|
 | 56    69    1     | 7     459   459   | 3     2     8     |
 | 57    289   28    | 1     29    3     | 6     457   457   |
 | 4     3     27    | 8     25    6     | 9     1     57    |
 |-------------------+-------------------+-------------------|
 | 367   26    4     | 2359  8     2579  | 1     57    69    |
 | 9     1     237   | 6     35    257   | 8     457   457   |
 | 8     67    5     | 49    479   1     | 2     3     69    |
 *-----------------------------------------------------------*

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Postby daj95376 » Thu Nov 20, 2008 6:24 am

The problem with forcing chains and DICs is that different paths may produce different results. Here's a path starting with [r2c2]=7.

Code: Select all
 a-b-c-d-e
 *-----------------------------------------------------------*
 | 37    5     378   | 29    6     279   | 4     89    1     |
 | 1    a47    9     |e34    347   8     | 5     6     2     |
 | 2     48    6     | 459   1     459   | 7     89    3     |
 |-------------------+-------------------+-------------------|
 | 56    69    1     | 7     459   459   | 3     2     8     |
 | 57    289   28    | 1     29    3     | 6     457   457   |
 | 4     3     27    | 8     25    6     | 9     1     57    |
 |-------------------+-------------------+-------------------|
 | 367   26    4     | 259-3 8     2579  | 1     57    69    |
 | 9     1     237   | 6     35    257   | 8     457   457   |
 | 8    b67    5     |d49    479   1     | 2     3    c69    |
 *-----------------------------------------------------------*

The XY-Chain or M-Wing would have been a better choice.
Last edited by daj95376 on Thu Nov 20, 2008 2:27 am, edited 1 time in total.
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Re: Double Implication Chain???

Postby ArkieTech » Thu Nov 20, 2008 6:25 am

Jasper32 wrote:
Code: Select all

I worked this puzzle to this point. In a "solver" it stated that by using either the (4) or the (7) in r2c2, the (3) in r7c4 could be eliminated. I can see how using the (4) in r2c2 can force r2c4 to be (3) hence the (3) in r7c4 can be eliminated. But I cannot figure out how using the (7) in r2c2 can force this elimination in r7c4. Is this a Forcing Chain or a Double Implication Chain or are the terms synonymous.

Any help is truly appreciated.
 
 *-----------------------------------------------------------*
 | 37    5     378   | 29    6     279   | 4     89    1     |
 | 1     47    9     | 34    347   8     | 5     6     2     |
 | 2     48    6     | 459   1     459   | 7     89    3     |
 |-------------------+-------------------+-------------------|
 | 56    69    1     | 7     459   459   | 3     2     8     |
 | 57    289   28    | 1     29    3     | 6     457   457   |
 | 4     3     27    | 8     25    6     | 9     1     57    |
 |-------------------+-------------------+-------------------|
 | 367   26    4     | 2359  8     2579  | 1     57    69    |
 | 9     1     237   | 6     35    257   | 8     457   457   |
 | 8     67    5     | 49    479   1     | 2     3     69    |
 *-----------------------------------------------------------*


xy-chain that solves the puzzle
r2c2=7=r9c3=6=r9c9=9=r9c4=>r2c4<>4
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Postby Jasper32 » Thu Nov 20, 2008 9:14 am

Below is a Nice Loop that I have a question about. I do not understand why r7c7 and r8c9 are not strong links since there is a (68) in both cells and no other (6's) or (8's) in box nine. And why r1c5<>5.

Thanks for you help on the above. I understand the logic concerning my original post. This has me baffled.

[R1C5]=8=[R1C9]-8-[R8C9]-6-[R7C7]=6=[R4C7]=3=[R4C5]-3-[R1C5] => R1C5<>3

Code: Select all
 
 *--------------------------------------------------------------------*
 | 2567   567    12     | 9      35678  357    | 4      1237   1278   |
 | 24679  4679   8      | 36     1      347    | 5      2379   279    |
 | 3      4579   149    | 58     4578   2      | 78     6      1789   |
 |----------------------+----------------------+----------------------|
 | 2456   456    7      | 1      235    9      | 236    8      2456   |
 | 2589   589    239    | 4      23578  6      | 237    1257   1257   |
 | 24568  1      234    | 2358   23578  357    | 9      2457   24567  |
 |----------------------+----------------------+----------------------|
 | 489    2      49     | 7      456    1      | 68     459    3      |
 | 478    3478   5      | 236    9      34     | 1      247    68     |
 | 1      3479   6      | 235    2345   8      | 27     24579  24579  |
 *--------------------------------------------------------------------*


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Postby hobiwan » Thu Nov 20, 2008 9:48 am

Jasper32 wrote:I do not understand why r7c7 and r8c9 are not strong links since there is a (68) in both cells and no other (6's) or (8's) in box nine.

Hello Jasper32,

I think it's a problem with notation again. You have to bear in mind, that in nice loop notation not all implications are spelled out.

8-[R8C9]-6-[R7C7]=6 means:
if r8c9<>8 => r8c9=6
if r8c9=6 => r7c7<>6 (weak inference)

You could of course use the strong inference on 6 or 8 between r8c9 and r7c7, but that would result in a different chain.


Jasper32 wrote:And why r1c5<>5.

I suppose you meant r1c5<>3?

The chain means: if r1c5<>8 then r1c5<>3. But if r1c5=8 then r1c5<>3 as well, so no matter how you look at it, r1c5 cannot be 3.

A different nice loop for the same elimination (for practice):
r1c5 -3- r4c5 =3= r4c7 =6= r7c7 -6- r7c5 =6= r1c5 => r1c5<>3
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Postby Jasper32 » Fri Nov 21, 2008 8:26 am

Thanks to you for your help and help it did.

I do have one question though. What is the determining factor when you have a row, column or box that has a conjugate pair whether you will use this pair as a weak link or a strong link? Is there a criteria that simplify the decision for me?
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Postby hobiwan » Fri Nov 21, 2008 12:23 pm

You can use whatever can help you to continue with your chain. If you need a strong link, use the conjugate pair as strong link, if you need a weak link, use it as weak link.

For more concrete advice I am the wrong person. Although I have spent some time now with my chaining algorithm I am still very bad at finding them myself. Perhaps one of the manual solvers can step in with additional hints.
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Postby daj95376 » Fri Nov 21, 2008 12:46 pm

Jasper32 wrote:I do have one question though. What is the determining factor when you have a row, column or box that has a conjugate pair whether you will use this pair as a weak link or a strong link? Is there a criteria that simplify the decision for me?

DAJ's Simple Guideline:

1) If you eliminate the candidate in one of the cells, then you will need to use strong inference ... and ... a strong link is necessary.

2) If you assign the candidate in one of the cells, then you will need to use weak inference ... and ... either a strong link or a weak link may be used.

Note: grouped strong links are strong links ... and they come in very handy when you encounter an ER pattern in a box!

===== ===== =====

Note: That's DAJ's Simple Guideline and not Simple DAJ's Guideline.:D
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