UHC 309 Rounds the Bases

The ultrahardcore review solvers illustrate a diverse solution path, before and after AIC and cluster building.

Here is the grid after the bypass and box marking.

Beeby found a naked single SE4 in r8c7 in its basic.

The Sysudoku Basic doesn’t look for them. See what you have to do to identify it here. Now would you want to do that for every cell?

In Sysudoku they come from construction, not search.

In the basic trace the naked single is the SE4 in the 8: trace.  Beeby’s hidden pair is NW46 in line marking, where it’s a reaction to NE4.

X-wings are caught in line marking. As you reposition candidates to mark line slinks, you glance over at parallel lines for matching pairs. When there’s more than a match, it could be a finned X-wing. Check out Sudokuwiki’s covering X -chain. It’s also made of line slink matches.

After basic, the lowest hanging fruit is usually unique rectangles marked by naked pairs. Of course ultrahardcores are gonna have hidden URs, with extra candidates, and enabling slinks in the UR values.  UHC 309 starts with these two.

For how it works, assume the victim is true and follow the consequences of the slinks.

To find one, watch for the embedded UR values in rectangles over two, not four boxes, and mark the slinks. Then pick the potential victim that produces a rectangle of UR values that can be interchanged without disturbing outside cells.

With that, Beeby begins a series of simple chain ANL with this pair. The black AIC can begin with 6r5c2 or 6r4c8. The black/red AIC may appear to be 1-way as an extension from 6r5c2, but it can be started from 6r8c1, and is two-way.

The AIC leave only 6r5c2 for W6.

This long ANL can start from either end as a 1-way, but finishes as an ANL. The ending is unpredictable. In DIY, all you can do is keep it going, but you might hold special nodes like ALS, or complex 1-way branches for the case where the simple chains produce nothing.

This one produces C2, and in DIY AIC building, it’s definitely better to suspend network branching to exploit the new clue.

The simple chain series ends with two long AIC ANL in the West boxes. First, a reverse bv AIC removes 4r4c1, gaining C4 and S4. C4 leaves a pointing pair r45c6, removing 7r7c6.

Now the  AIC is cut back from r1c1 to r1c4 and extended from 7r4c2 to 6r8c1 for an 6 ANL. If this were found first, the 4 clues of the 1 way would have occurred with the ANL.  We now get NW4 and NW6,

and what Beeby labels as a discontinuous loop. It’s not a 1-way, but another ANL with a group as a terminal. This brings to mind a reason why a Beeby sequence is not going to duplicate your DIY sequence of moves. Beeby’s is governed by its labeling of results, which is controlling what the user asks for. The DIY sequence is governed by the solver’s selection of AIC starting points, made without knowledge of AIC building results

Next is the first true 1-way. The 1-way logic  of 3r4c8 being false regardless of 3r7c8 doesn’t apply to a chain start from 4r4c8.

As  the second 1-way opens two new coloring links, a cluster is finally started, and expands as a finned 3-wing adds another 3-slink.

There’s a a lot to digest on the next grid. The 3-slink connects a second cluster. Beeby’s third 1-way is an ALS AIC. It must start at 6r8c1, with the assumption that 6r8c1 is false. The AIC then confirms 2r9c1 is true to make 6r9c1 false.

We’re not quite done. Beebe finds a long chain from 5r6c8 to 5r8c5 for an ANL, but noticing the cluster entry on blue 8r2c8, we slink directly to green 5r8c5 for a coloring shortcut.

Now the blue/green expansion traps 1r1c5, and Beeby’s long 1-way through the cluster is largely bypassed by coloring shortcut. We could slink directly from blue 9r9c5 to green 7r8c2, but that would leave no reason for starting with such a slink.

Still in search of a wrap, we get a long simple chain ANL with a coloring shortcut. In DIY the advantage of coloring is that once the chain enters a cluster, you get many options for the next slink.

Now, after after W7 implies C7 and SW2, we get three traps and E5 by red/orange expansion.

The 8r6c8 removal will leave blue and orange 8 alone in the West box. They are slinked, merging orange and green.

In the merged cluster, two green 1’s are forced in c3, wrapping green.

Next is 309 + 44 = 353

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.
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