SudokuSolver Forum http://www.rcbroughton.co.uk/sudoku/forum/ |
|
Example of Strong Link and Example of Connected Pair http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=5&t=675 |
Page 1 of 1 |
Author: | stef71 [ Wed Dec 30, 2009 11:30 am ] |
Post subject: | Example of Strong Link and Example of Connected Pair |
Hello to the list users. Although I am not a Sudoku beginner, I need to ask you two questions about two basic definitions. QUESTION 1: a strong link is a link between two candidates in a bivalue cell or a bilocation unit. Could you give me two separate examples, one for a bivalue cell and one for a bilocation unit? QUESTION 2: a conjugate pair is always a connected pair, but not all connected pairs are conjugate pairs. Could you please provide me a counter example? Thank you for your help Stefano |
Author: | Børge [ Wed Dec 30, 2009 11:55 am ] |
Post subject: | Re: Example of Strong Link and Example of Connected Pair |
Hi stef71, Welcome to this forum. Sudopedia is always a good resource for looking up basic sudoku definitions. stef71 wrote: QUESTION 1: a strong link is a link between two candidates in a bivalue cell or a bilocation unit. Please see examples 1 and 2 in my post Some tips for spotting XY-Chains.Could you give me two separate examples, one for a bivalue cell and one for a bilocation unit? stef71 wrote: QUESTION 2: a conjugate pair is always a connected pair, but not all connected pairs are conjugate pairs. Could you please provide me a counter example? I don't know of any off hand, but perhaps you can find something HEREHope this helps. Børge |
Author: | stef71 [ Sat Jan 02, 2010 12:03 pm ] |
Post subject: | Re: Example of Strong Link and Example of Connected Pair |
Dear Borge, thank you for your help. I read carefully your post "Some tips for spotting XY-Chains". Can I ask you few more questions? 1. I understand that in example 2 there is a strong link on 9 between cells r5c6 and r5c7. I think that also the links within the "neat chain" are strong links (for example strong link on 6 between cells r5c4 and r1c4, on 4 between r1c4 and r1c6 and so on). Am I correct? And the difference between the strong links within the neat chain and the link on 9 between cells r5c6 and r5c7 is that the former is a link between two cand idates in a bivalue cell, while the latter is a link between two candidates in a bilocation unit. Again, am I correct? 2. Always in example 2, could you help me spotting all the conjugate pairs? thank you again for your help Stefano |
Author: | Børge [ Sun Jan 10, 2010 6:54 pm ] |
Post subject: | Re: Example of Strong Link and Example of Connected Pair |
Hi again Stefano, stef71 wrote: Can I ask you few more questions? Sure, but sometimes it will take a couple of days before I am able to answer.stef71 wrote: I think that also the links within the "neat chain" are strong links (for example strong link on 6 between cells r5c4 and r1c4, on 4 between r1c4 and r1c6 and so on). Am I correct? Not completely.The XY-Chain in example 1 has six links. Four of them are strong links and two of them are weak links. Which two are weak links is left as an exercise. stef71 wrote: And the difference between the strong links within the neat chain and the link on 9 between cells r5c6 and r5c7 is that the former is a link between two cand This conclusion is correct.idates in a bivalue cell, while the latter is a link between two candidates in a bilocation unit. Again, am I correct? stef71 wrote: Always in example 2, could you help me spotting all the conjugate pairs? I have never had the need for using conjugate pairs.Based on the definition at http://www.sudopedia.org/wiki/Conjugate_pair I have found the following conjugate pairs in example 2. r=Row, c=Column, n=Nonet. Digit 1: r5, r6, c3, c5, n4, n5. Digit 2: r4, r6, c4, c7, n5, n6. Digit 3: r1, c3, n4. Digit 4: r1, r4, c4, c6, n2, n5. Digit 5: r4, r5, c3, c6, n4, n5. Digit 6: r1, r5, c4, c5, n2, n5. Digit 7: r6, r9, c4, c5, n5, n8. Digit 8: r5, r9, c4, c7, n6, n8. Digit 9: r5, r6, c6, c7, n5, n6. |
Author: | stef71 [ Thu Jan 14, 2010 7:46 pm ] |
Post subject: | Re: Example of Strong Link and Example of Connected Pair |
Hello Borge, I read carefully your precious answer, but unfortunately I am not able to spot the two weak links in the XY-Chain of example 1. It seems that I am not a good student, but it is just matter of time. The six links are: First link on 6 between the cells r5c4 and r1c4 Second link on 4 between the cells r1c4 and r1c6 Third link on 3 between the cells r1c6 and r6c6 Forth link on 9 between the cells r6c6 and r6c7 Fifth link on 2 between the cells r6c7 and r4c7 Sixth link on 8 between the cells r4c7 and r4c5 As far as I can understand, each of them works in the same way: At link 1, assumed 6 on the first cell, the choice of 4 on the second cell is forced At link 2, assumed 4 on the first cell, the choice of 3 on the second cell is forced At link 3, assumed 3 on the first cell, the choice of 9 on the second cell is forced At link 4, assumed 9 on the first cell, the choice of 2 on the second cell is forced At link 5, assumed 2 on the first cell, the choice of 8 on the second cell is forced At link 6, assumed 8 on the first cell, the choice of 3 on the second cell is forced Where are the two different links? Moreover I didn’t understand the list of the conjugate pairs that you wrote down. I am not able to understand what you mean. Again, just a single explanation and then I will carry on. Thank you for your patience and your help Stefano |
Author: | Børge [ Thu Jan 14, 2010 8:50 pm ] |
Post subject: | Re: Example of Strong Link and Example of Connected Pair |
Hello Stefano, stef71 wrote: Where are the two different links? That something is forced has nothing to do with strong or weak links.Here the definition of a strong link: A strong link exists between 2 candidates when one of them must be true. Strong links can be present in bivalue cells, in bilocal units and in Almost Locked Sets. For bivalue cells and bilocal units, a strong link also enforces a weak link. If the following logical deductions can be made for candidates A and B, they have a strong link:
Take a closer look at "Third link on 3 between the cells r1c6 and r6c6". If r1c6 = 3 -> r6c6 <> 3 -> r6c6 = 9. This since r6c6 is a bivalue cell, i.e. there is strong link between the digits 3 and 9 in r6c6. If rc6c = 3 -> r1c6 <> 3 -> r1c6 = 4. This since r1c6 is a bivalue cell, i.e. there is strong link between the digits 3 and 4 in r1c6. But this does not mean that there automatically is a strong link between the digits 3 in r1c6 and r6c6: Assume A is digit 3 in r1c6, and B is digit 3 in r6c6. A=false (r1c6 <> 3) does not imply that B=true (r6c6 = 3). B=false (r6c6 <> 3) does not imply that A=true (r1c6 = 3). This since r4c6 can be 3, i.e. there is more than two cells that can be 3 in column 6. For "First link on 6 between the cells r5c4 and r1c4" this is different: Assume A is digit 6 in r1c4, and B is digit 6 in r5c4. A=false (r1c4 <> 6) => B=true (r5c4 = 6). This since there now are no other cells in column 4, which can be = 6. B=false (r5c4 <> 6) => A=true (r1c4 = 6). This since there now are no other cells in column 4, which can be = 6. Hopefully you can now spot the second weak link in the XY-Chain in example 1. stef71 wrote: Moreover I didn’t understand the list of the conjugate pairs that you wrote down. Here the definition of a Conjugate pair:I am not able to understand what you mean. Again, just a single explanation and then I will carry on. A conjugate pair is a pair of candidates with a strong link. They are the last 2 candidates for a single digit in a house they share. Børge wrote: Digit 1: r5, r6, c3, c5, n4, n5. For digit 1 there is a conjugate pair in row 5, in row 6, in column 3, in column 5, in nonet 4 and in nonet 5,i.e. there is a strong link for digit 1 in row 5, in row 6, in column 3, in column 5, in nonet 4 and in nonet 5, i.e. thare are 6 different conjugate pairs for digit 1. |
Page 1 of 1 | All times are UTC |
Powered by phpBB® Forum Software © phpBB Group https://www.phpbb.com/ |