## Softening left page ultrahardcore 353

Here is another puzzle the DIY oriented solvers suggest is too hard for human solving, even as the moves they find are too instructive to ignore.  This post gets quickly to ALS methods that demand exhaustive enumeration from the DIY solver, and gets to coloring. A second post will exploit the expanding cluster in much less demanding ways to finish UHC 353.

Here is the grid after a very productive bypass. The givens are in the more formal font. The less formal is Bradley Hand ITC representing handwriting.

The basic trace shows clues derived from clues, to a point where 3-fill lines appear. One is resolved for the last basic clue.

The first advanced move is a 4 – ANL you could spot in line marking, when you are filling c2 and marking its 4 slink.

Next, spotting this  hidden unique rectangle is very unlikely. The UR slinks permit 9r8c4 to force 6 into adjacent corners, making a solution rectangle in which 6 and 9 can be interchanged for second solution. UR is based on the assumption that a Sudoku composer will not let that happen, and without a solver, that too, is unlikely.

Then the grouped 1-chain Sudokuwiki gets 1r8c7. Beeby gets that with a finned 1-wing.

Then Beeby goes to AIC building for a grouped ALS ANL with a 5 value set as an ANL terminal.

Now both solvers are held off, except for Beeby’s ALS methods.  Either you have the rare talent of spotting them as needed, or you go through the exhaustive ALS incremental mapping procedure outlined previously in this ultrahardcore series.

The first Beeby find is this ALS_95.

Next, a very related ALS wing, an AIC of ALS nodes strung together just like an XY chain.

Finally, a remarkable pair of  ALS wings. 5r5c1 is a single in blue and in orange ALS. 9r6c1 is a single in orange.

The two chains are detailed below.

The chain (1=5)blue – (5=9)red – (9=1)orange

is a confirming ANL removing 1r8c1. 1r25c1 is a value set in blue and orange ALS.

The chain

(8=5)blue – (5=9)red – (9=8)orange

is an ANL removing 8r3c1. 8r25c1 is a blue value set and 8256 is an orange value set. The Wr2 boxline removes 8r2c9.

Now the solvers’ paths continue more normally.  A second hard-to-spot hidden unique rectangle is followed by an easy 2-chain ANL that wipes the UR away if it comes first. It doesn’t matter, though because the 2-chain clue does the UR removal.

The 2-clue also enables a 9-chain ANL.

Beeby teams the box ALS with a new line ALS for an ALS_98. This might have been a demonstration that the incremental ALS _XZ construction can fail, but this one works even if 9r6c4 has not been removed, because the grouped common is valid.

Sudokuwiki gets to the same results with a different removal, with an APE.

Now we have reached coloring and have a trap, but UHC 353 is not giving up. So let’s close it out from here next week.