This post was updated in January 2023 to include guide examples found by Phillip Beeby’s PhilsFolly solver. It features novel POM analysis, unusual ALS_XZ, hard to spot hidden UR and multiple clusters converging on a collapse.
The hidden UR show up on the line marked grid. The corner values are 38 and 45. It’s the slinks that signal the UR presence.
Holding off on AIC, there’s a Sashimi swordfish. Instead of a third 6 candidate, one column has two in place and a third, the fin, which is seen by a potential victim. 6r2c2 is a fin because its presence spoils the fish. Its removal would restore a swordfish. Sashimi victim saves itself by seeing every fin, thus restoring the fish that victimizes it.
Independent of the swordfish, there’s also an ALS_64. The 6 singles see each other, and an outside 4 sees the singles in each ALS.
An AIC ANL extends in both directions for another removal.
Next, Beeby delivers a Pattern Overlay removal with the message:
“Between them r4c5 and r5c9 include all patterns of 4, so patterns of 6 which include both cells can be deleted. As a result, no pattern of 6 includes r5c9 so 6 can be deleted from r5c9.”
In this two-step process, first find an X-panel with every pattern containing one cell or one of two cells. On the 4-panel, r5c9 is a second cell contained in all patterns missing r4c5.
Between them, cells r7c1 and r7c9 are also included in all 4-patterns, but two cells on the same crossing line cannot be on the same pattern.
Now the 6 panel reveals that any West to East freeform starting at 5c9 hits r7c8 and r1c7 and ends a r6c1. Tracing back, East to West, the only ff including r5c9 also includes r4c5, so this pattern includes the two cells in all 4 patterns. 6r5c9 is eliminated in step 1, as this pattern is deleted.
Next, an AIC ANL is extended to form an ANL with a slink on the chain.
The ANL extension party continues with a third one
After a seventh AIC ANL, two more POM eliminations.
On the first, the Beeby says, “Between them r7c8 and r9c3 include all patterns of 7, so patterns of 6 which include both cells can be deleted. As a result, no pattern of 6 includes r5c1 so 6 can be deleted from r5c1.”
On step 1, a South to North ff not started on 7r9c3, must include 7r7c8.
In step 2 on the 6-panel, the single pattern containing both cells that makes it also includes r5c1, so 6r5c1 is deleted.
On next POM, “Between them r2c5 and r6c1 include all patterns of 6, so patterns of 9 which include both cells can be deleted. As a result, no pattern of 9 includes r2c5 so 9 can be deleted from r2c5.”
West to East ff’s starting at r3c1 (not r6c1) cannot hit r1c5 or r3c6, and therefore must hit r2c5.
Every 9 pattern including both includes r2c5, but there are patterns including r6c1, but not r2c5. So 96c1 is not deleted.
Now an easy ANL brings N9 and an unusual ALS_73.
Then almost the same ALS in an ALS_75, followed by a 1-way.
A cluster provides a shortcut for a 1-way at the top, and a grouped chain ANL at the bottom wraps blue.
Unbelievably Wex 427 fights on. We add a red/orange cluster.
Then an aqua/pink, then a purple/yellow. We get an aqua/yellow bridge trap for
C7 => (N7, r9s34).
A Sashimi 3-wing takes 3 from r5c5, duplicating the trap, and another victim sees the fin.
A final ANL leaves
And the colorful solution
Systematic Sudoku 