Single Alternate SdC on ultrahardcore 1

This post reports a rare outcome in an SASdC trial, the extra term carrying through to a solution.

Here is the grid with NWc1 marked as a Single Alternate Sue de Coq chute. The contents of the wall can be described as

NWc1 =

(5+6)(3+4) + 342.

The bv 56 says 5 and 6 cannot both be in the chute, so one of them is present, requiring  3 or 4 to also be there., unless 5 and 6 are both missing.  The SASdC trial is testing for exactly that.

If the extra term fails, then the NWc1 becomes a normal Sue de Coq removing extra 5 and 6 candidates from the NW box.

The trial gets off to a great start, with a double hidden unique rectangle.

Each row slink in the rectangle produces a reversible rectangle solution if the opposite side 5 is present. Beebe sees one, and deletes a 5, but that destroys the hidden UR on the other side.  We don’t expect a solver AI to hold the effect of one 5 until it tests the effect of the other one, but we oversee the removal of both.

Going back for c1s67 => SW5, Beebe begins AIC building with this remarkable assembly of parts. Continuing the XY chain from r1c5, Beebe recognizes the aligned pair as a slink partner in the ANL, one it can “see” in the C box.

Now the XY chains get easier and build more bv. An ANL with an Er6 boxline.

They keep coming, another easy XY ANL.

Another bv means another XY node, but it also means more resources for coloring.

One more.

Now a red/orange cluster stops the drip, drip, drip.

r6c6 => not

(orange and green)

and

r5c9 => not

(red and green)

So (orange or red)

=> not green

Now following the arrows, blue 1r1c5 => 2r1c9 => orange .

Instead of a contradiction,  the trial produces the solution.

Next week’s post demonstrates another type of trial with ultrahardcore 1, combining coloring and pattern analysis.