The New Sudoku Players' Forum

[Cec]

Thanks ravel - I found your explanation was clear. I don't know whether it's just me but I would welcome forum adoption of some uniformity in the notations used for these various solving techniques. My suggested notation for this example would be either:
r1c4=[27] > r4c4=9, r4c7=7, r3c7=5, r3c2=2 OR
r1c4=2or7> r4c4=9, r4c7=7, r3c7=5, r3c2=2

PS. Noticed Sped has just responded two minutes after my above thoughts. Thanks Sped. Past my bedtime over here. I'll look at this tomorrow.

Cec

[Sped]

Hi Sped,
Your above notation refers to five cells and six candidates (2,7,9,7,5 and 2). Could you please explain your interpretation of this notation.
Cec

Sure.

2-(r1c4)-7-(r4c4)-9-(r4c7)-7-(r3c7)-5-(r3c2)-2

The chain starts at r1c4 and links on 7 with r4c4, which links on 9 with r4c7, which links on 7 with r3c7, which links on 5 with r3c2.

The 2s on the ends? There is an unlinked 2 leading into in r1c4 and an unlinked 2 leading out of r3c2. Any cells that see both r1c4 and r3c2 can have their 2s excluded.

I see this chain as having 5 bivalue cells:

2-(r1c4)-7
7-(r4c4)-9
9-(r4c7)-7
7-(r3c7)-5
5-(r3c2)-2

It has unlinked 2s on both ends, so it can lead to the exclusion of some 2s.

[emm]

I agree that the notation is confusing Cec –

I’d see this as chains
r1c4=2 -> r3c6=7 -> r3c7=5 -> r3c2=2
r1c4=7 -> r4c4=9 -> r4c7=7 -> r3c7=5 -> r3c2=2
so r3c2=2

Or a loop
r1c4-7-r4c4-9-r4c7-7-r3c7-5-r1c9-7-r1c4
so r1c4<>7

[Sped]

Can someone explain the accepted notation for expressing XY Chains?

Code: Select all

*--------------------------------------------------*
 | 25   9    3    | 27   4    6    | 1    8    57   |
 | 1    7    4    | 8    5    3    | 2    9    6    |
 | 6    25   8    | 1    9    27   | 57   4    3    |
 |----------------+----------------+----------------|
 | 3    25   1    | 79   6    4    | 79   257  8    |
 | 279  6    279  | 5    8    1    | 479  3    247  |
 | 8    4    579  | 3    2    79   | 6    57   1    |
 |----------------+----------------+----------------|
 | 4    3    27   | 6    1    5    | 8    27   9    |
 | 57   8    6    | 29   3    29   | 457  1    457  |
 | 259  1    259  | 4    7    8    | 3    6    25   |
 *--------------------------------------------------*


There are XY chains all over the place in this grid.

Here are two more, using the notation that makes sense to me:

5-(r4c2)-2-(r3c2)-5-(r3c7)-7-(r3c6)-2-(r8c6)-9-(r6c6)-7-(r6c8)-5

It's a chain of 7 cells, with unliked 5s on each end. It allows the elimination of the 5s at r4c8 and r6c3.

2-(r9c9)-5-(r1c9)-7-(r3c7)-5-(r3c2)-2-(r1c1)-5-(r8c1)-7-(r7c3)-2

It's a chain of 7 cells with unlinked 2s on each end. It allows the elimination of 2s at r9c1, r9c3, and r7c8.

Either one will solve the puzzle.

How would these chains be described in the standard notation? Once I understand that notation I will post future chains both my way and the standard way.

Thanks.

[emm]

Have you read Jeff's v. good explanation here ?

Edit : Ravel's link is even better.

[ravel]

Sped, this is the first thread i found about xy-chains. There were no nice loops at that time. So i dont care about "right" notations, i just want to be able to follow one easily. I am happy with yours as well (as soon as you had explained it once). All the names and specifications are confusing me more than any solution for a puzzle written in any logical way.

[Sped]

Have you read Jeff's v. good explanation here ?

Edit : Ravel's link is even better.

I saw that. It explains things very well. The diagrams are especially helpful.

But I never understood the notation he used.

It seems like he's trying to express xy chains in nice loop notation. I don't understand nice loops.

He says: "Nice loop notation always starts from the discontinuity:" And the example of the XY chain he gives starts with the cell that gets candidates excluded.

Sorry, but that is not how humans go hunting for XY chains. When you look for the chains you only have a vague idea where the exclusions might occur.

You pick a starting cell, note its unlinked candidate, and go looking for a chain that ends with the same candidate.

The important information is where the chain begins and ends and what the unlinked candidate common to both ends happens to be.. Cells that see both ends can have that candidate eliminated.

That's why I like my notation. It expresses the important information very clearly.

But as soon as I figure out the standard notation I will express chains both ways.

[ronk]

Can someone explain the accepted notation for expressing XY Chains?
......................
There are XY chains all over the place in this grid.

Here are two more, using the notation that makes sense to me:

5-(r4c2)-2-(r3c2)-5-(r3c7)-7-(r3c6)-2-(r8c6)-9-(r6c6)-7-(r6c8)-5

It's a chain of 7 cells, with unliked 5s on each end. It allows the elimination of the 5s at r4c8 and r6c3.

2-(r9c9)-5-(r1c9)-7-(r3c7)-5-(r3c2)-2-(r1c1)-5-(r8c1)-7-(r7c3)-2

It's a chain of 7 cells with unlinked 2s on each end. It allows the elimination of 2s at r9c1, r9c3, and r7c8.

But I never understood the notation [ed: Jeff] used.

It seems like he's trying to express xy chains in nice loop notation. I don't understand nice loops.

He says: "Nice loop notation always starts from the discontinuity:" And the example of the XY chain he gives starts with the cell that gets candidates excluded.

That's actually quite funny ... because if you had added a discontinuity to the end of your chains, you would have had Jeff's nice loop. Your expressions above would look like:

(r6c3)-5-(r4c2)-2-(r3c2)-5-(r3c7)-7-(r3c6)-2-(r8c6)-9-(r6c6)-7-(r6c8)-5-(r6c3) implying r6c3<>5

AND

(r9c13)-2-(r9c9)-5-(r1c9)-7-(r3c7)-5-(r3c2)-2-(r1c1)-5-(r8c1)-7-(r7c3)-2-(r9c13) implying r9c1<>2 and r9c3<>2

Oh ... Jeff uses square brackets instead of parentheses, but that's irrelevant IMO.

CAVEAT: Having not seen your chain notation for conjugate links, I can't express an opinion there.

[Sped]

That's actually quite funny ... because if you had added a discontinuity to the end of your chains, you would have had Jeff's nice loop. Your expressions above would look like:

(r6c3)-5-(r4c2)-2-(r3c2)-5-(r3c7)-7-(r3c6)-2-(r8c6)-9-(r6c6)-7-(r6c8)-5-(r6c3) implying r6c3<>5

AND

(r9c13)-2-(r9c9)-5-(r1c9)-7-(r3c7)-5-(r3c2)-2-(r1c1)-5-(r8c1)-7-(r7c3)-2-(r9c13) implying r9c1<>2 and r9c3<>2

Oh ... Jeff uses square brackets instead of parentheses, but that's irrelevant IMO.

CAVEAT: Having not seen your chain notation for conjugate links, I can't express an opinion there.

Here's what I don't get.. in the 1st example, what's so special about r6c3?

6 cells see both the start of the chain r4c2 and the end of the chain r6c8. r6c3 is just one of them.

All six cells (r4c7,r4c8,r4c9,r6c1,r6c2,r6c3) can have their 5s excluded.

Are we supposed to write the chain six times, once for each exclusion?

[ronk]

Here's what I don't get.. in the 1st example, what's so special about r6c3?

It's a deduction ... a conclusion ... an exclusion ... and elimination ... a consequence of the chain. A chain with no consequence is pretty useless.

Are we supposed to write the chain six times, once for each exclusion?

Group the exclusions and you'll need to write it twice at most. Besides, usually other exclusions follow with simpler techniques anyway.

[Cec]

Sped, this is the first thread i found about xy-chains. There were no nice loops at that time. So i dont care about "right" notations, i just want to be able to follow one easily. I am happy with yours as well (as soon as you had explained it once). All the names and specifications are confusing me more than any solution for a puzzle written in any logical way.

I'm appreciating the help from all of you but seeing I raised the issue of "right" notations - or words to that effect - then it's probably me that should be targetted rather than "fista-cuffs" developing between others

The way I now see things, if I fully understood about xy-chains, loops, etc. then it's highly likely that I would have understood Sped's notation. I note ravel agrees with this view in his reply to Sped in saying "I am happy with yours (notation) as well (as soon as you had explained it once)." However, as I don't understand these techniques, the different wording of notations can be confusing.

I can easily follow em's above notations on chains and loops but I'm unsure whether these two notations relate solely to the xy chain in question. If they do then I would prefer this simpler notation.

ravel's reference to Jeff's xy-chain description and example seems a good place for me to learn and, in hindsight, perhaps I should have concentrated more on understanding these techniques rather than trying to improve notations which describe them.
Cec