This post does Basic and reports humanly practical results from the two review solvers on ultrahardcore 179. Then for a stall breaking trial, we turn to the limited value patterns, and their discovery through the X-panel view and freeform drawing. These become easy value pattern trials aided by coloring in the following post.
UHC 179 gets the stingiest bypass award in the ultrahardcore review, and is in contention for the busiest line marked grid.
The possible hidden UR’s in c78 lack the necessary slinks. But Beeby starts it off with a finned 2-wing in c58, with a 2 cell fin. The victim sees both cells of the fin, so if it were true, it would remove the fin and therefore validate the X-wing that makes it false. The finned fish victims literally can’t win for losing.
Both solvers find the 3 – ANL, and Sudokuwiki gets the finned 2-wing removal with a grouped ANL.
Next we’ll take Beeby’s simple 1-way from 7r1c8, and Sudokuwiki’s dfc ALS boomerang from 8r2c9, which Beeby duplicates with an ALS-wing.
With Beeby getting into ALS wings and Sudokuwiki into forcing chains, we get this ANL with one terminal an ALS value group. It’s also a form of 1-way.
One more bv is gained by this ALS -wing, with bv r9c6 as the third ALS.
But it is also time to look for reasonable trials. I was scanning the X-panels for new X-chains and fish, but now it’s time to scour the panel edges for limited value patterns.
Below is the so far undisturbed 8-panel. We’ll walk through the process that uncovers a limited set of patterns that can be the basis of a trial.
A pattern is a set of candidates, each one being the single candidate in a box and two lines, that provides a candidate for every box and line. Each pattern can pictured as a segmented line drawn from one side of the panel to the opposite side, which crosses every candidate of the pattern. We call these freeforms, for the graphic element that is a segmented line.
The possible patterns are most clearly seen when freeforms are drawn from the side that most limits how they can start. On the 8-panel, North to South freeforms start the first two lines in 4 ways. South to North, i’ts 5 ways. East to West freeforms start two lines in 2 ways. Also notice that many candidates are left out of patterns starting either way. When all patterns are identified, any candidate not on a pattern can be removed. I call them orphans.
It requires patience, but there is a systematic method for mapping out all patterns. Let’s say we start with 8r2c9, going East to West. We pick a favored cross direction to go for the next segment, say North. Starting in r2c9, for column c8, we must go to r5 because NE has an 8. Then we veer back in the favored direction for c6. For c4 it’s r7 to avoid a second 8 in the C box, and to get an 8 for the S box. For c3, the first two rows have their 8’s, and we go to r7 and back up to r3 for c2
When we see that no 8 is available for c1 and the SouthWest box, let’s note there is an interchange between columns 2 and 3 on the last two rows, because there is an alternate 8 in both remaining rows. That makes it easy to see a second freeform getting just as far.
To find the first pattern, we work back along the columns and down the rows in each column looking to continue from every unused candidate. In c3, we can take r8 in place of r6. What happens in c2, though is, r3 leaves no landing place in on r6 and, and r6 leaves no landing place in r3
Next back continuation is r8c4. It produces two freeforms to c1r7 and two more failures.
Finally the patterns through r6c6 and r8c6, for a total of 6 patterns.
So what have we learned by mapping out the patterns from 8r2c9? For one thing, there are no more candidates other than 8r5c8to be added to the trial, because they join these two in every pattern. Also, we have the information to make inferences from any addition or removal of 8 candidates in the trial.
We can make single trial of a pair of patterns in the diagrams by coloring the two candidates that differ, but it still takes up to four trials. Each is likely to be decisive, since in each trial a large number of 8 candidates are removed. Only eight 8 candidates remain in each trial. But if all four trials fail, we likely have up to four more on the patterns which include 8r2c9.
Next post, we’re going to explore a pattern trial alternative that is often better, but in the meantime, you get homework. The 5-panel at this point has a limited number of freeforms starting from the East side. Your job is to enumerate them, lay them out, so that the number of patterns can be counted, and they can be assembled into fewer trials.
Of course, the longer term challenge to find a solution of another right page ultrahardcore without trials is still on the books.