This updated post describes how I-41, in Extremely Hard v. 10 by Rebecca Bean, after one bent region concession to two Gordon Fick ALS_XZ and a BARN, demands extensive AIC building, but rewards the updating bv map and X-panels on every removal.
Here is the basic trace, starting with an unresolved 3-fill.
In the original post, my Canadian co-hort Gordon Fick found this classic ALS_XZ. A grouped restricted common enables 1r7c9 to see all 1’s in both green and blue ALS.
Gordon noted that the other participating bv, could be the ALS partner in another ALS_XZ.
Want to figure that out? I’ll reveal it at the end of this updated post.
The first advanced method I found is an AIC almost nice loop eliminating 1r7c9.
Coming back in 2022 with the PhilsFolly solver, there’s a noteworthy set of AIC’s, beginning with this boomerang starting with the r5 5-slink. Then, tracing this backward from 9r6c8, the 1-way red 9 branch extension removes two 9-candidates.
Then a 1-way from 1r2c7 becomes an ANL in black, when I get a gift that Beeby’s coding does not anticipate. The ANL termnals wink for a much more effective nice loop. Beeby finds it when asked for an AIC.
The cleared c7 makes the next 1-way possible. Why isn’t it an ANL?
From here, Beeby finds several routes to a coloring finish. The least likely DIY route starts with this ALS_17. You might look for cross line common values for ALS r459c9 and find more of them by by going out to r7c46789
The cluster expansion traps 7r8c9, and allows ALS_25,
and ALS_96, both plausible through bv partnering.
ALS_96 removes 6r4c6 and adds 58r4c6 to the bv map. Either ends Bean Extra Hard 10 i41.
The removal permits a swordfish confirming blue in r8.
The new bv adds this very long and decisive XY ANL to the railway.
Going back to just before the unlikely-to-spot line crossing ALS_17(4 grids back), AIC building continues with a 1-way aimed at the 8’s.
Then an easy shortcut for a bv.
The removal looks harmless,
until you see the naked triple.
And the steep collapse to confirm blue.
Next week, the review is concluded with a few unreported highlights, starting with IV-12 here. Come prepared with your basic trace.
After that, the plan is to post several reports on the develop activity on the Sysudokie Guide, a set of pages on Sysudoku methods and related issues. The Guide is accessed via the menu bar above.
Now about Gordon’s other ALS in Bean’s Extremely Hard I-41. Another grouped restricted common is the key. If any candidate could see all the 4’s, it would go, as well.
But you know, I also missed a BARN, a bent almost restricted n-set, in this case a 4-set. Only the 1’s are “bent” in the bent region Ec7. A BARN is a spotting signpost for a bent n-set type 1, or BNS1. Here, 1 is the only common value in the bent region remainders.
Systematic Sudoku 