## UHC 355 Provokes a SASdC Trial

After a typical ultrahard Sysudoku Basic,

Sudokuwiki starts with an APE so unusual as to change my working definition of the APE. APE stands for Aligned Pair Elimination.  From every example so far, I thought it was the two elimination cells that were aligned in a row or column. No, it’s that two cells are simultaneously aligned with ALS that can prohibit any combination of two candidates, one from each cell, that see two of the ALS’ value groups. If every combination of a candidate in one of the cells is so prohibited, it is false.

Here,  every combination of 7r9c7 with 2, 4 and 9 in r7c1 is prohibited. The blue ALS stops 27 and 47. The red ALS stops 27 and 29. One way to avoid repeating work is to list every combination of the two cells, then cross out combinations stopped by the ALS seeing both cells. There are 4 combinations of 2 with other values, and 10 combinations of other values with other values. A policy for a reasonable human search for APE is complicated.

Sudokuwiki, the computer code, has no such problem with APE. Four combinations to filter through the ALS this time.

It may be the number of ALS and cell pairs that’s more of a problem. How many combinations this time? Only 5.

Next, Sudokuwiki adds this AIC ANL with an ALS node.

Then it identifies 3r8c6 as a pattern orphan, without explaining why. We analyze the 3-panel, looking for a humanly possible  way to do this.

The 3-panel reveals a limited number of West to East freeforms crossing r8c6: 3 from r2c1 and one from r3c1. Looking for a toxic orphan. Note that those visiting r8c6 must also visit r9c7. Among the X-panels, we don’t see another  whose every pattern must visit these two cells.

But  Beeby’s note identifies 9 as the restraining value.  Of the five East to West freeform enumerated 9 patterns, three are stopped by 3r6c5 and the other two by 3r5c9. So 3r8c6 is a toxic orphan. After announcing the orphan, Sudokuwiki gives up. Switching to Beeby, we get the same result, but with the APE’s handled differently. You can’t prescribe candidates to either solver, only given clues, so we get to see Beeby redo the APE eliminations.

First, the 7r7c4 is an ALS_37.

Then 2r7c7 disappears via a grouped ALS_42.

The 7r2c4 removal takes an ALS wing, which can also be interpreted as an ANL with the slink chain with two or three ALS nodes.

Then after identifying the toxic orphan 3r8c6, all the Beeby methods fit for human computers are exhausted, and its trial time.

The  Sysudoku bv scan reveals Single Alternate Sue de Coq NW3 = 9(6+7)(2+5) + 952. If the trial fails, the remaining SdC NWc3 = 9(6+7)(2+5) eliminates 6r2c1 and 6r3c1 in the NW box. We add a small cluster.