This post begins a series on alternative approaches to trials of base cell solutions of an exocet. This one applies the chute lettering to UnSolvable 190. Then, instead of immediate exocet trials, it begins a systematic resolution of its 8 pattern, which ultimately generates the solution.
Drawing straws for an exocet trial is not the only systematic way to cut an Unsolvable fog of candidates. Alternative fog clearing techniques are illustrated in this drawn out fight with Unsolvable 190.
As usual, we start with the line marked grid, appropriately marked with the double exocets identified by JC Von Hay on the Saturday of publication on Andrew Stuart’s Weekly Unsolvable page.
The basic solving is hard, but the trace makes it look easy, because it accomplishes so little. The monster fog of candidates is upon us.
An exocet is a trial generator. In my man vs. beast contests with the Golden Nugget and Fata Morgana monsters, I found inference chains connecting the base and target solution digits for constructing decisive trial sets. The solution of the puzzle is definitely a solution of the exocet cells, but is it necessarily an exocet? It is generally accepted as such, and I’m just a believer. All I’ve seen are examples, no proof.
When an exocet is recognized in a monster fog puzzle, one progressive step is to see if an exocet solution is possible. In particular, can extra digits in the exocet band or stack be arranged to allow one. That is the purpose of the chute table seen here.
In the double exocet stack above, the contents of the chutes are, besides the exocet digits a, b, c, and d, the extra digits 2 and 5. The 2 and 5 distribution, down to the chute level, is determined by whether or not r5c3 =2 and r2c2=5. The table shows the four cases, with the solution digits of the blue exocet base cells designated as ‘a’ and ‘b’.
Only one of the four cases places a or b in the two blue targets. And it also places c and d correctly in the green exocet.
So now going forward, we have this distribution of 2 and 5 candidates on trial. This lifts the fog slightly, and brings a few bv into view.
The Sysudoku Order of Battle (SOB) calls for the bv scan when bv are available, well ahead of exocet trials. The reason is that up to five long and involved trials are possible. Any simplifications beforehand will pay dividends. On that score, lettering will be extended to the whole grid for 190 and possibly, for other Unsolvables later in this series.
From the 8-panel, here are the West to East freeforms of the two blue and 4 green patterns . Is the pattern more likely to be in green? Yes, so I try blue, for the more likely contradiction, and a more decisive, if smaller, victory.
This time, the trace to a contradiction is not too long, and there is an opportunity here to see how the trace, which is done, and read, while candidates are melting away, is then graphically represented on the full grid to document the trial.
In words, one path of clues forces 3 in r8c8. A branch confirms 3r2c1, forcing 3 from r5c1. The blue 8 and the 4 it triggers eliminate 8r5c7 and 4r5c1, leaving the naked pair 67, which takes out 7r5c8.
The message for you:
I did not “find” or “spot” any of this. I used ordinarymarkup in a conventional order, writing it down in a trial trace. Then I went back to the original copy of the grid, and drew arrows and “seeing” lines down the direct paths to the contradiction.
Think about it.
Anyway, that leaves four patterns for the remaining 8’s, which slinks divide into two competing teams, red and orange. Continuing with the orange trial, delete the 8’s not on an orange freeform. Next time, we continue with this logarithmic reduction to a solution, then look at alternative paths. Maybe you’d like to hammer out the orange trial, and even choose a red alternative for the final push. Word of warning: it’s a challenge. With any luck at all, you’d have a solution in four trials.
Do you, by any chance, like this systematic grinding down of a puzzle taken to be unsolvable by advanced techniques? Oh no! You might be a closet sysudokie.