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Correcting Dan's typos:

W-Wing: (4=6)r3c5 - r3c4 = r46c4 - (6=4)r4c6 => r3c6,r5c5<>4

I don't see what can be Wrong! with asking a question. Let me put it another way. If r3c6 contains only the two candidates <35>, why on earth would you write (3-5)r3c6?

The Wrong! was in re ...

Help me here:

(3=5)r3c6 says r3c6 is a bivalue cell. Right?

(3-5)r3c6 says what??

Wrong!

(3=5)r3c6 says there's a strong inference between the candidate <3> and the candidate <5& ...

Thanks Danny, I will try and digest your working definitions, but I'm having trouble seeing how a bivalue can be both.

A bivalue cell is neither a strong inference nor a weak inference. There's onl ...

I don't think that last sentence is very accurate.
It was a failed attempt at "whimsey". Someone use to repeat the conclusion of discontinuous loops ... and I thought it was you. Sorry!

Here's my "working definition" of strong inference and weak inference.

Strong Inference: When you have two possible outcomes and you assume that one outcome isn't true, then you must ...

A discontinuous loop that produces eliminations in [c1] and [b7].
+--------------------------------------------------------------------------------+
| 5 469 1 | ...

I found Angus Johnson's post from 2005 here. I had forgotten his "Type 3" was for simple coloring, which we don't have in this example. Perhaps it is X-coloring, but I can't check that out r ...

+-------+-------+-------+
| . . . | . . . | / . . |
| . . . | . . . | / . . |
| . 28. | . . . | 2 . . |
+-------+-------+-------+
| . . . | . . . | / . . |
| . . . | . . . | / . . |
| . . . | . ...

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

M-Ring C (6=7)r1c5 - r3c56 = (7-6)r3c8 = (6)r3c56 - loop => r3c8<>3; r12c4<>6

r12c48 <39> UR Type 1.2223 <> 39 r2c4

You me ...

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

Impossible it ain't.

+--------------------------------------------------------------------------------+
| 267 25678 2358 | 369 67 1 | 4 35679 567 |
| 46 ...

[Withdrawn: I was mistaken about the specifics of AJ's Type 3 Simple Coloring.]

I also used the DP 49 in boxes 258. Either r1c4 or r6c6=6 or r9c6=8. Common outcome; r4c6=6.
r6c6 = 6 implies r4c6 =6? How can that be? They are in the same column.

If r6c6=6 is false, then it's ...

My solution is very similar to Dan's, so I looked for a totally different alternate but, after spending more than an hour, gave up.

Danny, if you read this I would be interested in what your progr ...

Then, I saw we were slicing and dicing this every way possible.

The same reason for my post.

Another "simple" example for using the <79>UR. (Almost the same as Keith's solution.)

after basics
+-----------------------------------------------------+
| 4 8 3 | ...

Ted,

Thanks! Much easier to reconstruct.