A Second Cluster for the HM Easter Monster


This post continues the Hanson and Barans attack on their Easter Monster with trials of a slink between the 4/6 candidate loops in the W and S blocks. The pair of trials required to do this will either prove the expected link, or solve the puzzle, as described in the previous post.

HMEM bluegreenYour homework first. Here is the 3/7 blue green cluster, which has no effect on its own.

Hanson and Barans select 4r6c2 and 4r8c4 for their “synching” trials, but give no reason for this choice. It would make sense to pick the pair having the creating the largest expansion of blue/green, because if they are wrong, a trial of two candidates must go all the way to a solution.

In that regard, the choice is a good one. The 3 and 7 candidates removed by the 4 and 6 clues extend the blue/green cluster into complete 3 and 7 patterns.

HMEM color XYZI do my first bv scan now with the fog somewhat dispersed, and it turns up something new about coloring. The 38r7c9 wing’s 8-candidate sees the hinge 8 because it is green. If the wing 8 is true, the hinge 3 is true. The victim in r4c5 sees the 38 wing 8 via an Andrew Stuart cell forcing chain.

Any other 8 that sees green also sees the hinge and wing 8’s, so we can look among those seeing 8r3c5. Sure enough, 8r3c4 forces a 2 in and a green 7 out of r1c4 and is dismissed.

Three more XYZ wings are dead on arrival.

Hanson and Barans state that “a more complex analysis involving almost-locked sets concludes that blocks 4[W box] and 8[S box] are also linked as shown”. I didn’t find ALS chains forcing blue to see blue, or green to see green, or ALS toxic sets removing blue or green. Maybe you can. But in Hanson’s earlier writing, ALS covers a lot of ground, including XYZ- wings and fishing. So perhaps, the above is what they meant.

HMEM both 4 trialsAnyway, the four blue and green color trials for both true and both false are routine. The both true blue trial leaves two 1’s in r7. The much simpler green trial excludes 8 from C5.

 

 

 

 

 

HMEM both false 4The “both false” 4 trial reached an impasse, again with complete 3 and 7 patterns. Here is another opportunity to look for the ALS resolution that Hanson and Barans claim.

 

 

 

 

 

HMEM blue 9-wingInstead I went fishing on the blue color trial, and found a 9-wing(red), and a 1-chain(purple). The three wing removals were useless, but the skyscraper removal in C forced two 2’s into c2. Of course this was actually found by a 2-D trace.

 

 

 

 

HMEM both false greenIn the green both false trial, a small, but nice loop removes 5’s in c5, leaving 5 marks in S which prove a 5 in SE, covering an 8-candidate and triggering a boxline removal in SW.

I had colored a 5-cluster left by this for color trials, when I realized that the nice loop gave me an opportunity to use a nice loop trial instead.

However . . .

HMEM nice loop ANLthe AIC expansion of the nice loop in the clockwise and counterclockwise directions got out of hand, generating ANL for four removals.

It’s enough to make trials unnecessary, forcing two 5’s into r4.

So we now have rejected that the two 4’s are alike in being both false, and we have the Hanson and Barans slink between them.

HMEM green trial traceNext time we continue with a red/orange cluster to join our attack on the HM Easter Monster. If you’re going for it now, start with 4r6c2 in red.

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About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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