Bean Gets No Second Extreme

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.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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