This post demonstrates the Single Alternate Sue de Coq with Castillo’s Only Extreme 218. The opportunity for this kind of trial is spotted early in the bv scan, but is best deferred until it is needed as a last resort. Only Extreme puzzles certainly qualify as possible candidates for the SASdC.

Sue de Coq is based on a logical description of a chute as three factors, one a clue and two binary factors, the alternates. In classic Sue de Coq there are two ALS in the box and line remainders of the chute, each ALS matching the two numbers of an alternate factor. The true candidate must be in the factor or in the matching ALS, and can be removed from any other remainder location.

In the single alternate form, only one of the alternate factors is matched by an ALS. This match allows only one of the matching number to be in the chute. If one is indeed present in the chute, one position is left for the two unmatched numbers, and removals of the matched numbers can be made in the remainders. A trial determines if both matched numbers are missing.

We pick up the solving of 218 right after basic, in the scan for APE and Sue de Coq. You could be on the lookout for ALS-XZ and BARN as well.

In SEc9, the possible contents are 9(5+7)(1+6) + 9(16+61), the first term being the classic Sue de Coq with the alternate (5+7) present, and the second, its contents with alternate values 5 and 7 missing. The SASdC trial follows up what happens if the alternate values are missing. If this trial reaches a contradiction, then the regular Sue de Coq is in force, removing 5r1c9 in this case.

What happens is a bit unusual. Instead of a contradiction or a collapse to the solution, the trial makes some updates, and stalls. We must continue from there

We look up to realize the “missing alternate” being tested has placed the 8’s and added bv and slinks to open up coloring. We dutifully add another tan/yellow cluster to take up the slack, and look for overlaps for bridging and merging of clusters.

It’s easy to conclude that if

not(orange and violet) and not(red and violet) then not violet.

Yellow quickly confirms both orange and blue, and the solution pours out.

The trial of missing matched numbers in the SASdC is often decisive. I think you would agree, that logic based trials are far better than arbitrary guesses, or abandoning the puzzle. Done too early, trials risk concealment of advanced logic and put a cap on learning.

As a last resort, a trial temporarily concedes that the puzzle is extreme.

Next we take another leap of faith, to Only Extreme 261. Four to go.