## An Orphan Takes Down Nakamoto Extreme 163

In this post, AIC building is replaced by BARN’s, conventional chains, coloring, and a noteworthy pattern analysis result.

Nakex 163 basic starts with a 3-fill. The bypass contains six more. Two resolve into clue and naked pair, and one, into three bv.

We include the first advanced move, a unique rectangle, on the line marked grid.

The signpost for the UR is the r8 naked pair.  Then we examine the extra candidates. In this case, the extras complete a naked pair.   A DIY rationale is that, if either 5 or 6 is true, the bv will force both values out of the ceiling corners of the rectangle.

Nakex 163 goes 143 one better, by responding to the bv scan, with BARN’s as well as XY chains.

BARN’s are difficult to spot. The signpost is the naked appearance of four values in a bent region, likely noticed in scans for Sue de Coq or XYZ-wings.

The long XY ANL puts itself together on the bv map XY railway.

In the follow up marking, railway ANL removing 2r3c7 and 8r9c8, are overtaken.

That was so nice,

how about another BARN and long XY combination? It’s a 4-BARN 1579 before the ANL, or a 3-BARN 159, leaving out r8c3, after.

The ANL removal 7r9c3 brings Sudokuwiki  a WXYZ, which we insist on calling a BARN. The bent region is Sr1 and just the right selection of cells is required to make it work. The long 1-chain removing 1r6c4 is followed by an 8-chain eliminating 8r6c5.

Sudokuwiki finds a slink chain branching off the 1-chain, and removing 1r6c6, which it interprets as a red/orange simple coloring.

Row 2 has blue seeing red, showing that not(blue and red)  implies green or orange.

On top of all this, the 9-panel has a slink network we can express as a blue/green cluster. Can we expand this cluster by pattern analysis?

Looking at the West to East freeforms, we can say that if blue is true, 9r1c3 and 9r7c1 are true. But this isn’t enough to extend the cluster to them, because blue may be false. If green is true, the green candidates  in c1 and c3 are not determined. The blue extension is not valid because there is a green freeform that reaches r1c3 and r7c1.

Fair is fair, so let’s try a freeform expansion on the red/orange cluster.  If orange is true, the orange candidate is determined in columns 2, 3 and 4, but none are decided by a red verdict.  In c5, the red candidate is limited to the North box, and the orange candidate to the Center box. That leaves 1r3c4 an orphan. It’s left out regardless of which is true, red or orange.

Take it out along with the removals above, and blue/green takes over.

First N5 => C5. Then the new r1 7-slink enables the 7 – ANL.  Then the orphan 1r3c4 removal triggers a huge expansion of blue/green which we keep going beyond the blue wrap in r7c3 and r9, and the red wrap in c9.

A remarkable wrap up of Nakamoto Extreme 163.

Next is Nakamoto 183, the final review puzzle.