The New Sudoku Players' Forum

[Luke]

I might be a bit old fashioned, but isn't Leren's M-ring also called a 'nice' loop?
pjb

Yep, a continuous nice loop. All weak links conjugate, which means in this case r3c9<>5 for completeness.

You don't hear the term "nice loop" much any more, as few use nice loop notation.

[daj95376]

The M Ring I found in this puzzle is a Type A as described in this link.

Hmmm! One of us has your M-Ring type wrong. I show it as the first M-Ring found below.

Code: Select all

 M-Ring  B (6=1)r7c8 - r7c9  = (1-6)r3c9 = (6)r3c8   - loop  =>  r3c9<>5; r89c8<>6
 M-Ring  B (6=1)r7c8 - r23c8 = (1-6)r3c9 = (6)r789c9 - loop  =>  r3c9<>5; r89c8<>6
 M-Ring  C (6=1)r7c8 - r7c9  = (1-6)r3c9 = (6)r789c9 - loop  =>  r3c9<>5; r89c8<>6
 M-Ring  D (6=1)r7c8 - r23c8 = (1-6)r3c9 = (6)r3c8   - loop  =>  r3c9<>5; r89c8<>6


To my knowledge, the "ring" is an old term that many now call a "loop". Since ronk went to the trouble of formalizing the M-Wing and M-Ring patterns, I believe that it was his choice to use "ring" instead of "loop".

To me, a "nice loop" is associated with nice loop (NL) notation. A notation that ronk still uses at times ... along with HoDoKu. For Eureka notation, I choose to simply use "loop".

Finally, the UR pattern that I listed is not my own. Mike Barker created numerous examples classifying UR patterns. I simply copied the example that I thought applied. I also (manually) filled in his pattern name to the output from my solver, which uses very generic information about URs that it finds. There are several UR eliminations present in the grid, I originally listed the one that I felt was most important. Here's what my solver found.

Code: Select all

 r28c46  <78> UR via s-link              <> 7    r2c4
 r28c46  <78> UR via s-link              <> 7    r8c6

 r37c89  <16> UR via s-link              <> 1    r3c8
 r37c89  <16> UR via s-link + non-UR     <> 5    r3c9
 r37c89  <16> UR via s-link              <> 6    r7c9

 r79c14  <35> UR via s-link              <> 3    r7c1


Regards, Danny

[storm_norm22]

i'd like to clarify something in my previous post about loops. I was saying how the nodes must start and end in the same house. the chain must also come back to the same number candidate. so for example if the chain starts on candidate (3)r3c8, then the chain then must declare a strong inference on another candidate 3 in row 3 OR column 8 OR in the same box.

that would then form a loop.

[David P Bird]

i'd like to clarify something in my previous post about loops. I was saying how the nodes must start and end in the same house. the chain must also come back to the same number candidate. so for example if the chain starts on candidate (3)r3c8, then the chain then must declare a strong inference on another candidate 3 in row 3 OR column 8 OR in the same box.

that would then form a loop.

What you describe is about three quarters of the meaning of a loop in Eureka notation.

An AIC loop is formed when the last node in a chain is connected back to the first using a link that follows the alternating pattern.

Your definition requires that the chain starts and ends with strong links to instances of the same digit that see each other, but misses out the case when the two candidates are different but occupy the same cell.

To round things off; to prove an inference between the first and last nodes of an AIC chain, these nodes must be connected to the chain by the same type of link. The usual case is when the links are strong when the two nodes must contain at least one truth, but if the links are weak the chain proves that they can only contain one truth at most and at least one of them must be false.

The weak link form can be used when the nodes overlap so that if (a)r12c3 - ...... – (ab)r12c3 is proved, then r12c3 <> ab.
If final node is true the first must be true too which is invalid, so only the first node can possibly be true.

[storm_norm22]

but occupy the same cell

right !! yes !! bingo !! yahtzee !!

I didn't cover that last bit because the subject at hand was same house as in row, column, box. but you are right. same cell, same outcome. very good.

you should definitely post something in the half m-wing thread on the daily forums, that thread needs some big time explanations. and while you are at it, all the other AIC commentary in those forums. you would definitely have your work cut out for you.

just ask daj, wink wink.

[David P Bird]

daj95376, Leren, I've spurned UR memorising pattern eliminations before believing that they could always be expressed as AICs using one of three derived inferences, and therefore I would locate them using a chain hunt. The three derived inferences are:

1) (ab)side1 – (ab)opposite side2 - most common
2) Xwing(a) – Xwing(b) - reasonably common
3) (a#2)diagonal1 – (b#2)diagonal2 – rare, uses links on adjacent sides

However this 3U/2SL UR elimination can't be expressed as an AIC using any of these as far as I can see. It's a perfectly acceptable pattern though, so it means I must memorise it – DOUBLE DRAT! It also means I must check for any others like it TREBLE DRAT!

you should definitely post ..... on the daily forums.

I've enough trouble trying to defend the faith here thank you very much!

[David P Bird]

In a discussion (18 months later!) <DAJ pointed out> that there is a way to derive the UR inference from an AIC:

Code: Select all

 *-----------------*-----------------*-----------------*
 | 39   379  6     | 1    <2>  57    | <4>  <8>  35    |
 | 13   47   <5>   | 478  <6>  478   | 39   19   <2>   |
 | 12   24   8     | <9>  <3>  45    | <7>  156  156   |
 *-----------------*-----------------*-----------------*
 | 69   69   2     | 34   5    34    | <1>  7    <8>   |
 | 8    <5>  <4>   | 2    7    1     | <6>  <3>  9     |
 | <7>  1    <3>   | 6    8    9     | 2    45   45    |
 *-----------------*-----------------*-----------------*
 | 356  36   <9>   | 357  <4>  <2>   | 8    16   1367  |
 | <4>  236  1     | 378  <9>  3678  | <5>  26   367   |
 | 2356 <8>  <7>   | 35   <1>  36    | 39   2469 346   |
 *-----------------*-----------------*-----------------*

(1)r2c8 = (16)r3c89 -[UR]- (16)r7c89 = (6)r7c12 - (6=1)r7c8 - Loop => r3c7 <> 1, r7c9 <> 6

In this case, because the loop closes, the (6)r7c9 elimination becomes an added bonus to the regular pattern elimination.

A simple conjugate chain then finishes the job:
(6=1)r7c8 - (1)r7c9 = (1)r3c9 - (1=2)r3c1 - (2)r9c1 = (2)r9c8 - (2=6)r8c8 => r39c8,r89c9 <> 6 ste