In this post, Beeby leads the way, but the instructive methods bring us only to a partial value pattern trial. The trial date is next week.
After the usual slink marking Sysudoku basic,
ultrahardcore 135 has a busy grid:
But like 91, there’s something on it to find. That tease would prompt me to look for unique rectangles, the most explicit spotting opportunity. There’s the 2 and 4 rectangles r46c29 and r46c49, but the slinks aren’t there. Then maybe the 8 and 9 rectangle r46c36? No, too many boxes and also short on slinks.
The review solvers find us the same clue in different ways: The Sudokuwiki, with a confirming ANL in black, and the Beeby, with a 1-chain eliminating ANL in red.
I’m happy to have a few bv, and mark one connected slink pair,
but Beeby takes the steering wheel with an overlapped ALS_62, and
a grouped ALS_13.
On my part, I filed away this Single Alternate SdC NWr1 = 4(8+9)(2+7) + 274 for a possible trial later.
Beeby expands my pitifully small cluster with a complex 1-way from 1r4c7 with four (count’em) AIC enabling branches.
Fortunately, my attention is drawn to my 7-panel by the hidden unique rectangle below .
On the Limited Pattern Overlay charts below are two very telling sets of West to East value pattern freeforms on the 7-panel, after the 7r9c7 removal. There are only two 7 patterns containing 7r1c2. Can you check me out on what limits them? Both of them also contain 7r2c8 and 7r5c9
After 7 in c2 is placed, there are many patterns containing both c3 7’s. I’m showing only the 4 from 7r8c3, but you can trace out more. That’s how things are with this form of pattern analysis.
Bottom line, the trial of 7r1c2 runs with three clues, and without 10 of the 7-candidates. If it fails, it places one clue and removes one candidate. Is this intuition or logic? To me it’s logic, based on the earned facts on the 7-panel. Such a trial gains as much information per unit effort as the searching required by the strictly logical methods seen in this review.
Trial logic has another factual component in this case. Sudokuwiki soon turns to cell and unit forcing chains, then stalls. Beeby offers a MSLS that goes beyond the formula that Phil cites on philsfolly, the Beeby solver site. So we’ll count on more research or reader help, and report on the value pattern trial and its solution for 135 next time.
It’s a possibililty for that ultrahardcore right page trial free solution. Send one in and I’ll draw the grids and publish it to your credit.