## A Colorful AIC Feast

We are met today to confirm the AIC take down by sysudokie readers on a tough steer,  Megastar Maestro 49 of Fall 2009. The rodeo begins with limited coloring, the identification of five AIC hinge cells, and an extension of a 6-chain found earlier into the almost nice loop (ANL) shown here, confirming NE2=>NW2.

The new bv 49 and the reduction to four candidates in chute NEc7 brings us to consideration of

NEc7 SdC = 2(5+8)(4+9).  Can 58 be missing?  The answer is “No”, and a 4-candidate is thereby removed from r1c8.  The new bv 49 also adds a hinge cell, setting off an AIC exploration, leading to:

Another AIC confirming ANL , yielding NE9.  Do you see the extraordinary truth about AIC coloring that Maestro 49 is showing us?

Yes!!!

For the AIC five step path along the cluster from green 7 to blue 6, we can substitute a single slink.  Can it be true?

It is.  Once it is established that a cluster cannot be entirely removed, there is a slink – and a wink, if you need it – between any candidates of opposing colors, matching numbers or not, by definition of “strong link”.  It is astounding how little known this is.  Tell ‘em where you read it. Feel like letting Maestro 49 off the hook for being so informative?  No, we must be merciless.  Puzzles, like corporations, are not people.

The confirmation is fairly productive:

NE9=>(E9=>(C9m, C3), NE4m=>E4m=>SE4t).

As always we update the bv map and X-panels, looking for further implications.  The 9-panel yields a great 9-chain aka sashimi 9-wing aka 9-skyscraper. This produces

SW9=>(NW9m, W1bxln, SW2=>(r7nt467=>r7np35, Wbxln4=>SW4m)).

In updating the grid, I happened to notice the 5-chain from the colored 7 up to the region of the hinge cell containing a green 7. It’s another ANL with the same shortcut slink.  This one also has something new to say.  The toxic ends of the AIC are candidates of different numbers!  Don’t worry, the almost nice loop with converging winks undeniably exists, and the 5-candidate is history.  It is the wink inside the AIC hinge r3c7 that makes this possible.

Despite the encircling AIC lariats, Maestro 49 is refusing to collapse. We will continue in the next post, giving you an opportunity to anticipate what is in store. Add a second cluster, red/orange, starting with a red 1-candidate in r1c1, and update your bv map.  An XY wing enables another AIC.

## 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 and tagged , , , , . Bookmark the permalink.

### 1 Response to A Colorful AIC Feast

1. Bernadete says:

i like your articles so much. please try to post them more frequently.