## A Long Path Begins in ultrahardcore 311

This post begins a series of three, reporting moves by the human oriented review solvers Sudokuwiki and Beeby on Stefan Heine’s UHC 311.  Maybe you can shortcut this long path and a trial, but it allows me to illustrate human engineered ALS XZ finding and ultimately,  a new pattern analysis trial technique.

Ultrahardcore 311 yields no clue in to the bypass, and doubles down in box marking, leaving basic with two naked singles, a naked pair, and a more typical number of slinks and bv.

The line marked grid is remarkably playable, considering the very long fill strings.

Sudokuwiki starts advanced with a grouped “digit forcing chain”, more accurately classified by Beeby as a 1-way from 4r3c6. .  The starter sees the victim, and if true, it removes 4r4c6 directly. If 4r3c6 is false, the inference chain confirms 6r4c6, with the same effect.

Another dfc by Sudokuwiki notes. It is an AIC ANL, in Sysudoku Advanced sequence, and would come in AIC building. It could start at either terminal.  For simpler graphics we  omit the closing winks on the almost nice loops.

This grouped boomer from 4r3c6 confirms N4.

Another dfc AIC ANL, or what  Beeby calls a “simple chain”.

Sudokuwiki finds this ALS_65!   And then gives up.

The ALS spotting problem for the human solver is the large number of ALS, and the difficulty of seeing ALS_XZ pairs at once

A systematic approach is to maintain an ALS_XZ map showing only the ALS having two value groups that are single or aligned for possible Z and X with other ALS.

Here’s an ALS_XZ map at this point. Every ALS is contained in a line or box so three or four colors are enough to distinguish them within their unit.

The Z value groups in each ALS must see each other completely. The X value groups must be seen completely by some outside candidate.

In r1, no curves are drawn for r1c47 ALS 236 or r1c457 ALS 2356. Each as a Z=6, but no X restricted common with r8c1579 ALS14568.

Instead of redrawing the ALS_XZ map on each move, a more practical approach is to bring the updated ALS_XZ slide along as you solve, updating it on each move, and keeping an ALS on the map as long as a potential Z and X value groups are available.

Sudokuwiki found single 5 of r1c247 ALS 2356. Its ALS XZ algorithm must do some kind of limited search. Beeby’s ALS search is more exhaustive.

Next week, we continue from here with Beeby on this long November march.