This post checkpoints the finish of the tenth and last review puzzle of the KrazyDad Insane collection on www.krazydad.com. I also have a summary table for comparison with previously reviewed collections, and some observations about this excellent collection. My hat’s off to Krazydad’s dad, Jim Bumgardner. I’m grateful I didn’t have to eat it.
Finishing the line marking after the naked single, I pick up the potential Sue de Coq of NWr1, with contents 7(3+4)(5+8)+437. The 437 occurs if the alternative (5+8) is missing. The trial of NWr1 = 437 included the testimony of four forcing chains which prove 437 guilty of removing all three 4-candidates from the South box. This verdict removes one 5 and two 8-candidates. The ALS 158 in NW gets to keep its 5 and 8-candidates to match the SdC alternate (5+8). No guesswork there.
My next “find” was the potential Sue de Coq Er4 = 2(6+8)(1+9) +129+921, which has to be tested for the missing 68 of the extra terms.
The trial in this case ends in a “not guilty”. The (6+8) alternative, which would have made an indecisive removal of two candidates in E, is indeed missing. Failed test, but successful technique that produces the solution you see on www.krazydad.com . If the verification that a Sue de Coq is a Sue de Coq generates the solution instead of a contradiction, is that a guess? Hardly.
Gladly or sadly, the review is over. The KrazyDad Insane collection does Jim Bumgardner proud. It is indeed in the sysudoku extreme class, and deserves your enthusiastic support and attention. The summary table below, in comparison with the earlier ones in this blog, makes that point. Only four of 10 are solved without using some form of LPO, the sysudokie extreme weapon. One of those, Insane 465, demonstrates nice loop coloring, a new advanced technique. Who knows what other wonders lurk in this collection?
Why is the Insane collection tougher than the advanced level collections reviewed earlier? My opinion is that it is primarily the imbalance of candidates across the numbers, with an a few numbers having an unusually large sets of candidates. A direct effect on basic solving is the scarcity of naked singles, and other locked sets, making line marking hard, and usually devoid of removals. Advanced techniques are starved as well. The count of bv after basic solving is roughly half that of the advanced level collections. There are relatively few slinks, with poor X-panel and coloring opportunities. ALS with single pair restricted commons are rare.
One reason why the LPO techniques succeed in this environment is that they focus on and combine the patterns of numbers on the thin side of the candidate imbalance. When the imbalance is extreme, the LPO analysis can discover orphans, candidates belonging to no patterns. A demonstration is coming up soon .
I made much of the guessing issue as the review began. The arbitrary guess of one cell value was demonstrated to be unnecessary for the Insane collection. It would probably fare poorly with the Insanes because, quite frequently, an arbitrary guess will be indecisive and require backtracking over successive guesses. The review also revealed the hard won nuggets of logical truth in the collection that is hidden by arbitrary guessing. Those who guess their way through hard puzzles and claim to be solving them might as well just look up the solution and copy it.
I believe the Insane collection does require trials, not guesses. I hope the review made the case that trials of cluster colors and long inference chains should be deferred while reasonable alternatives remain. But clearly, labels of “trial and error” or “guessing” do not apply to trials which are initiated to verify a Sue de Coq, a unique rectangle or any other solving technique, even though such trials will occasionally reveal a solution. I’m glad this occurred with the second trial of Insane 4X5. It can be accepted as practical reality, undeserving of controversy.