This post reports how the Beeby solver comes to life after the Single Alternate Sue de Coq trial , and nibbles Heine’s ultrahardcore 223 to a second coloring cluster.
Beeby notes the ANL as a simple chain, but it’s AIC building class, with two cell wink nodes.
Then a relatively simple ALS_63,
is followed by the ALS_42, whose construction challenges drawing, and much moreso, spotting.
Now imagine spotting this double ALS_68, so called because there’s two restricted commons. Each ALS gives up a value, one 6, the other, 8. Other value sets in each ALS contain a true candidate.
The naked pair C49 implies W4, and a “discontinuous loop” takes another nibble. As in ANL, we can omit the weak link closure that breaks the AIC sequence,. The wink from 1r2c6 is direct, “seeing” in c6 when it is true.. The wink from 9r6c7 comes from the 1-way AIC when 1r2c6 is false. This chain is used again later, when intermediate removals make it more damaging.
Meanwhile Beeby’s “complex” chains get a workout. These have to be 1-way’s because the branches that make way for the chain exist in one direction. It is Phil Beeby’s baby. Humanly possible, under sufficient pressure.
Leaving from 1r4c6 one branch removes 1r9c4, and the other, 2r9c2, allowing the chain to confirm 1r9c2, if 1r4c6 is false, that is. Either 1r4c6 or 1r9c2 is true.
A second discontinuous 1-way nibble,
and another simple 1-way,
and Beeby throws another complex curve ball. No need to trace this one out for anyone.
The complex removal enables the 2 chain ANL,
and the simple 1-way from 5r8c5, whose 5r8c2 removal leaves a NW c1 boxline removing three 5s in NW, which picks up a 5-wing removing 5r9c4.
Now the hognose chain returns as an ANL, but with a second cluster. The clash of red and green in r4c2 means that orange or blue or both are true. The clusters share value 3. Any 3 seeing orange and blue is false.
Let’s save the finish of this overlong path for next week. If you go back to the last clue, you can run Beeby (philsfolly.com) and see how the action looks in text form.
Systematic Sudoku 
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