This post was updated in January 2023 to include guide examples by Phillip Beeby’s PhilsFolly solver.
A generous bypass makes Basic line marking easier.
A starting cluster and an obscure hidden unique rectangle appears in line marking.
Two slinks from a single corner let 4r5c8 generate a reversable rectangle.
Next, crossing ALS create an ALS_89.
After 1-way shows that 9r5c3 is false regardess of r9r6c1 being true or false, Beeby comes up with a pattern overlay (POM) removal of 7r5c3, saying that
“Between them r5c3 and r7c9 include all patterns of 5, so patterns of 7 which include both cells can be deleted. As a result, no pattern of 7 includes r5c3 so 7 can be deleted from r5c3.”
Looking at West > East freeform panels, every W>E ff missing r5c3 hits r7c9, confirming the first statement. The 7-panel shows that the only 7 W>E freeform crossing r5c3 and not r8c9, also crosses r3c6 and excludes both starting cells.
So there is no 7 pattern crossing r5c3. The 5 patterns make 7r5c3 an orphan.
The 7 removal allows another ALS to intersect the red ALS above, for another ALS_89.
The removal brings a Finned Sashimi 9-wing on r36. “Sashimi” refers to the fact that a corner cell is missing from the 9-wing. Both of the fins are seen by 9r6c6. Without the fins, 9r4c4 becomes a clue, and so does r6c1. The fin induced removal is not fishlike. It’s more like a 1-way AIC. If victim 9r6c6 is true, the fins are erased and the X-wing disintegrates into two clues on r3 and r6, one of which erases the victim. So the victim can’t remain true
Next, Beeby responds to a POM request with a removal that truly exceeds human solving limits. I report it for illustration.
The message reads, “Between them r2c1 and r6c2 include all patterns of 8, so patterns of 4 which include both cells can be deleted. As a result, no pattern of 4 includes r6c2 so 4 can be deleted from r6c2.”
In this case, verifying this result with freeforms is difficult.
Every 8 N>S ff missing r2c1 and reaching r9 hits r6c2.
Every 4-pattern missing r2c1 fails or misses r6c2.
It gets easier, as an AIC ANL wraps blue.
After the wrap, Beeby supplies a real fish, a finned 9-wing in c67. 9r5c8 sees the fin, and potential victims 9r5c4 and 9r8c35 don’t.
Another fish request brings a finned mutant 9 swordfish, with a base of three lines, and a cover of one line and two boxes.
One base 9r4c3 is not covered, but covered 9r8c3 sees it.
On a POM request, Beeby announces that 9r8c5 is an orphan. There are enough 9 candidates left to make that tough to confirm with freeforms, but . . .
It can be more easily shown that West to East freeforms all miss 9r8c5, by grouped forcing chains from each c1 starting candidate.
Adding a cluster, a shortcut ANL removes a critical candidate 4r6c9 and the follow up wraps orange, . . .
for the solution of Weekly Extreme Competition 428.
Systematic Sudoku 