This post and the next checkpoint a sysudokie solution of Antoine Alary’s extra tough More Extreme 200. Sysudokie readers are given an opportunity to get a little extreme, as well.

Happy St. Patrick’s Day. Let’s do the 200. But first, your kraken analysis homework on More Extreme 144:

Yes, the other 6 in the fin box is removed, but the four kraken hostages escape.

The basic solving of More Extreme 200:

It’s a semi –monster all right.

The next result is from the X-panel, and is quite unusual. A simultaneous, finned 7-wing and 8-wing, but no krakens.

That’s all I see for X-panels, coloring or AIC, but the 9-candidates are relatively sparse, with slinks in both directions.

Going to pattern analysis, I have two pink and five olive, with many 9-candidates in one set or the other. A trial of the pink set of patterns could take a big step.

In fact, in the trial of pink patterns, the two 9-candidates in both are confirmed, and the seven exclusive to olive patterns are removed.

As luck would have it, the trial fails with three bv 36 cells in r9. The true 9 pattern is among the olive five

The olive trial brings in only one clue, 9r5c5, but removes two. C9 generates a boxline in S. It’s 3 removals in S allows a Sue de Coq.

The contents of Sc5 are 3(2+6)(7+8) if 7 and 8 are not both missing and the naked triple236 if they are missing. But the latter generates three bv 36 cells in r9. So the Sue de Coq is verified to contain 3(2+6)(7+8), removing 78r2c5.

Now, how would you like to do the next pink/olive pattern analysis? The remaining 9 patterns can be divided again.

To be sure of agreeing with the checkpoint, make 9r2c6 pink and shade the 9 cells accordingly. Two clues are added in the olive trial, but only one in the pink trial, so we do the olive trial first, hoping for a more decisive result. As usual, you have a week. Lay off the Paddy’s day cache.

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## About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), father of 3 wonderful daughters and granddad to 7 fabulous grandchildren.

Here is an alternate solution. This alternative uses two Almost Locked Sets in a strategy often called Doubly Linked ALS-XZ.

There is an excellent description of this method at:

http://hodoku.sourceforge.net/en/tech_als.php#axz

I am specializing the description from the Hodoku website above to the puzzle at hand [More Extreme 200].

This alternative solution can start with the puzzle at the stage where our blog author notes above : ‘It’s a semi-monster all right’.

Consider the following two Almost Locked Sets:

ALS1 : The 3 cells in row 9 with columns 1,7 and 9 contain candidates 3, 6, 7 and 8 [this is an Almost Locked Set of 3 cells containing 4 candidates]

ALS2 : The 4 cells in column 8 with rows 6, 7, 8, and 9 contain candidates 2, 3, 7, 8 and 9 [4 cells containing 5 candidates]

There are only two possibilities for 7 and 8 in these 2 Almost Locked Sets.

1) 7 is in ALS 1 and 8 is in ALS 2

2) 8 is in ALS 1 and 7 is in ALS 2

[Notice that ALS1 cannot contain both 7 and 8 and similarly ALS2 cannot contain both 7 and 8]

For both cases, we see that we can exclude 7 from r8c9 and 8 from r7c7 because we know 7 and 8 must be in Box 9 and we know that 7 and 8 must be in either ALS1 or ALS2.

Now suppose case 1 obtains,

Looking at ALS1: r9c1 and r9c2 form the locked set {3, 6} [ provisionally excluding {3, 6} in r9c5 ];

Looking at ALS2: ALS2 is the locked set {2, 3, 8, 9}[ provisionally excluding {3, 9} from r1c8 ]

Now suppose case 2 obtains,

Looking at ALS1: r9c1 and r9c9 from the locked set {3, 6} [ again provisionally excluding {3,6} in r9c5 ];

Looking at ALS2: ALS2 becomes the locked set {2, 3, 7, 9} [ again provisionally excluding {3,9} in r1c8 }.

So now we know in either case 1 or in case 2, we can exclude {3, 6} in r9c5 and {3,9} in r1c8.

But we know that either case 1 obtains or case 2 obtains. So the exclusions are not provisional. Making a total of six exclusions: r8c9 is not 7, r7c7 is not 8, r9c5 is neither 3 nor 6 and r1c8 is neither 3 nor 9.

With these exclusions, the puzzle becomes relatively straightforward needing nothing tougher than some Naked Pairs and some W-Wings.

Of course, I make no claim to the originality of this alternative solution using Doubly Linked ALS-XZ. Further, identifying Almost Locked Sets like ALS1 and ALS2 remains a difficult challenge for human solvers. It is, though, my experience that ALS-XZ are not rare but quite prevalent. The doubly linked ones are probably less so. The very simplest ALS-XZ might be the ones that also go by the name WXYZ Wing. Andrew Stuart’s site gives a detailed tour through such:

http://www.sudokuwiki.org/WXYZ_Wing

Thanks again, Gordon. Your astute observations are a treat for me and all sysudokie readers. I’ll have grids to illustrate your comment and your other observations on Alary’s More Extreme 200 in my post of 5/5/15.