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[keith]

Another Menneske of the same ilk.

[Marty R.]

This puzzle kept me up past my already late bedtime. I must've missed some solution path because it took:

Type 1 UR
Two XY-Wings
Two XY-Wings w' coloring
Three W-Wings w' coloring
Simple coloring
And another XY-Wing w' coloring to finish it off.

[keith]

Marty,

The basics get you to here:

[Marty R.]

A couple of comments, Keith.

The BUG+3 reasoning is still something that is beyond me.

I arrived at a different ending position since I don't see the XY-Wing that, with coloring, finished it off for me.

I used the 58 W-Wing. According to my notes, I colored it for an elimination, then further colored it for another elimination.

And that 58 W-Wing--I assume you noticed--is more simply connected by the 8s in column 2. Regardless, I can't follow the chain of 8s, because there are three 8s in row 1, so how are r1c58 connected?

[keith]

[Marty R.]

Thanks Keith, I've printed out the grid and your explanations for further digestion.

[keith]

Marty,

When you have mostly two-value cells, and two or three three-value cells, the idea is this:

1. Check some element (row, column, or block) that has only two-value cells. Does each candidate occur exactly twice? If so, good. (If not, there is no BUG.)

2. Find an element that has only one three-value cell. Identify the two candidates that would make the DP, and the one candidate which would kill the DP. If you can do this, good. (If not, there is no BUG.)

3. Do step 2 for the remaining three-value cells, using the DP candidates found in step 2. If you can do this, you have arrived at the DP. All two-value cells, each candidate occurs exactly twice in each element.

4. You now have a list of cells and candidates, any one of which will kill the DP. Only ONE of them is necessarily true. It's up to you to figure out if this is useful information. Each case is different.

Some examples, for two three-value cells, a BUG+2:

a. Cell 1 is X OR Cell 2 is X. Like the pincers of a chain, any cell that sees both cannot be X.

b. Cell 1 is X OR Cell 2 is Y. Cell 1 = X forces Cell 2 = Y. Cell 2 must be Y.

By the way, I don't think this is very obvious. I stared at this thread's puzzle for a long time before I figured out that the BUG killers were saying R1C6 is not <6>.

Best wishes,

Keith

[Asellus]

I'm catching up after the holiday...

Completed this in 5 fairly simple steps without DPs:

1. Skyscraper R29 removes <8> from R13C9 & R8C8.
2. XY Wing, pivot R2C2, removes <5> from R3C89.
3. XY Wing, pivot R9C5, removes <5> from R9C4.
4. W Wing on {38} in B13 removes <3> from R1C8 & R3C1.
5. XY Wing, pivot R9C5, with Pincer R3C5 transported to R8C1 removes <8> from R9C9.

[re'born]

Here are three not so simple steps that lead to a solution:

1) xy-wing: pivot at r9c5 eliminates 5 from r9c4.
2) finned swordfish: c158/r138 fin r2c8 => r13c9 <> 8
After cleaning up, we get to