## Sudokuwiki Solves Only Extreme 347 by AIC

In the original Only Extreme review, OnEx 347 was an example of a coloring trial on a limited cluster generated by pattern analysis. In this update, Andrew Stuart’s solver demonstrates a solving path to a final coloring without trials, via AIC building.

The basic trace is updated to include 3-fills. In line marking, rows dominate with fewer unmarked cells.

On the line marked grid, the tight square of 5’s has the slink corner  for a hidden unique rectangle, Type 1.   If 3r5c7 is true, 5r5c7 is not, and two corners are 5, the other two, 3.  Now 3 and 5 interchange for a second solution.

Nothing is found in the bv scan or the X-panels,

before Sudokuwiki ventures into coloring with this trap. Both green and blue remove 9r2c7.  The resulting NEr1 boxline removes 9r1c5, expanding the cluster.

Entering AIC building, an AIC nice loop combines an XY-chain, a reversed bv, and two X chains, one grouped.

A grouped cluster expansion is accompanied by a long and winding AIC boomerang.

The removal enables a Type 2b uniqueness rectangle. If 9r1c2, the ur candidate opposite the slink is true, the other ur candidate 5r8c2 is true and 5r8c5 is false. The slink makes 5r9c5 true.

The 5/9 placements in the rectangle can be interchanged for a second solution copying this one everywhere else.

In the trap, 2r2c2 is rejected by both blue and green. And in the East, an XY boomer starts from r4c7.

Sudowiki piles on with a third AIC boomer, and after

an XY chain placing S5,

and                              after

the bv field looks ripe for another cluster.

The red orange cluster is extensive, but short lived. In r1, if red is true, both blue and green are false. Then in c7, if we accept orange, we have to take blue as well.

Next is the conclusion of the updated review of Emanuel Castillo’s Only Extreme Sudoku.

In case you want to try the last review puzzle OnEx 390 on your own, work with this  copy, because recovering the givens from the original review would give you too much in advance.