This post recounts another AIC building project of 15 boomerangs, Nakamoto Extreme 43. The Nakamoto Extreme collection justifies the ‘extreme’ label by possibly exhausting the time and patience of a human solver. Let’s say, if a puzzle justifies a trial for that reason, its extreme.
As often happens a short basic trace
signals a cloudy starting grid.
Before bringing out the boomerangs, Nakex 43 throws us an easy X-chain.
And here they come. Boomer 1 from 5r4c6 and boomer 2 from 9 r9c6. Even though both are X-chains linked by XY bv nodes, they are found in AIC building, where any means of extending a chain are employed.
Next come AIC boomers 3 from 8r1c4 and 4 from 6r1c6 => NWr1 boxline 2r3c2 and AIC boomer 5 from 1r2c8 creates NWr2 boxline removing 9’s.
Then AIC boomer 6 from 3r1c3.
The removal allows the former boomer path into 3r1c3 for an ANL removing 3r1c4. Then extension (red) from 8r1c4 closes ANL confirming 3r1c3.
The confirmed NW3 goes nowhere, but boomer 7 from 6r1c6 finds an ALS to get home, for N6.
After two XY ANL => NW9, an XY boomer 8 from 8r6c5.
Next, AIC boomers 9 from 9r8c5 and 10 from 2r5c8. The boomer 10 removal permits
a 6-chain ANL, and the new 6-slink in r5, which brings boomer 11.
The 6-chain removal also enables AIC boomer 12 from 6r4c9, and the boxline SEr9. To the left, the grouped boomer 13.
Sudokuwiki mislabels AIC bv boomer 14, from 2r1c1, as a digit forcing chain. The interpretation does not lead to a humanly practical way to find it. Viewing it as a boomerang does precisely that.
Sudowiki finds an APE requiring three ALS, a very unlikely human solving event. But the removal is not needed until much later.
Instead, the next AIC ANL depends on boomer 10.
The AIC ANL creates the c6 3-slink for a confirming bv boomerang 15.
the removal brings a long XY chain. But coloring is past due.
The cluster makes a shortcut example of the next XY chain, as the former XY removal enables a grouped 9 chain.
The 9-chain removal expands the cluster, trapping 8 to continue the expansion and force two blue candidates in r8c4. The green army cuts through the candidate undergrowth and lays out the Nakamoto Extreme 43 solution for us.
Thanks for sticking with a a very long post. I found no logical escape hatch, but perhaps you did. If so, clue us in. I’ll publish your comment, diagram your find, from your what and where, in a following post.
Next , another two post effort is Nakamoto Extreme 63. There’s another boomerang parade, then the first post ends it with Sysudoku pattern analysis and coloring, leaving the less spot worthy, but more spectacular, Sudokuwiki ending for the second post. You could follow the parade with Sudokuwiki, looking critically at your X-panels to see if you can get that first ending before it comes out here.