Cluster Maintenance Pays in Nakamoto Extreme 23

In this post, a cluster wrap interrupts the Sudokuwiki march on Nakamoto Extreme 23, with an abrupt collapse. The following post then follows the original solution through to another example of Andrew Stuart’s “digit forcing chain”, to note that human solvers can and should discard it.

The Nakex 23 line marked grid and basic trace:

After a quick scan for unique rectangles or remote pairs, a sysudokie constructs a bv map for XY chains and makes a copy for XYZ wings.

That is rewarded here with a inference chain i571-wing. Finding that a 17 bv is present to accompany the 15 wing, its not hard to find a 7-chain for the weak link. Sudokuwiki doesn’t do inference chain winks.

A coloring cluster looks promising. Green or blue removes 7r2c5.

The i571-wing removal is duplicated by an XY ANL following up the trap. Sudokuwiki misses both, but finds an APE removing 1r9c3.  ALS 157 prohibits 71 and ALS 129 bans 91. The two removals in c3 expands the cluster.




The cluster expansion traps 1r5c2 and provides a shortcut boomerang from 6r9c3, beginning a boomerang volley with boomer 2 below from 3r3c8 in black.






Boomer 3 in red branches off to come back at 6r3c8, and boomerang 4 (green) is thrown in the opposite direction from the 8-chain to another 3-chain.




The new bv 31r3c8 completes an XY ANL for NE3.








Then another boomer barrage, with boomer 5 from 2 r2c9 in black, boomer 6 from 9r1c9 in red,  boomer 7 from 1r1c2 in green, and boomer 8.







The 9r1c2 removal allows a grouped AIC ANL.





Next is Sudokuwiki’s grouped boomer with a group as the emerging slink partner.

The Sysudoku cluster reveals a remarkable coloring wrap. The red extensions create an inference chain weak link between cluster members of the same color.  If one is true, the other is false. Being the same color, both must be false, and blue is wrapped. Wow!!

From here, it still takes a naked triple, and two  1-ANL to wrap up Nakamoto Extreme 23.








Next post will forego the wrap and continue Sudokuwiki’s path to the end, for two purposes. First, to graphically reveal more beautiful boomerangs, and second, to reveal the Sudokuwiki “digit forcing chain”.  If you’re solving ahead of the blog for the feedback, here is an opportunity to find these gems on your own.





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.
This entry was posted in Advanced Solving, Extreme Solving, Nakamoto, Puzzle Reviews, Uncategorized and tagged , , , . Bookmark the permalink.

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