This post updates KrazyDad Insane v.4, b.7, #5 with a bypass 4-fill and a solution free of trials, unless you consider the complex 1-way a trial.
Did you look it up on the post of September 3, 2013 and find the 4-fill? That’s a line with four free cells in which you can make a placement by inspection. There are two possibilities, and one works. We amend the bypass trace to read
The remaining basic trace is unchanged.
To the line marking, we add Beeby’s UR. If 6r1c7, the 9 slinks carry 9’s to two corners, and the 6 slink carries 6 to the opposite corner. Then in a solution with that rectangle solution, 6 and 9 can be interchanged for a second solution.
Sudokwiki’s boomer 1 is followed by a grouped boomer 1, which Beeby duplicates with an ALS_31.
After Sudokuwiki’s 3rd boomer, you might well be starting a 1-way at 6r7c3, and extending the AIC with a branch.
You keep on, finding another branch and extending the AIC until you realize, the last branch that gets you the r3 slink also leaves no 4 for the NW box.
If the AIC is correct, then it started wrongly. 6r7c3 is true.
Now we have the second complex 1-way that ended the previous post. It’s worth scrolling back to ask, would I start this 1-way knowing that if it reaches a conclusion, it’s false and the starting candidate is true?
Well I wouldn’t. Starting with 6r2c1, I would be looking for a boomer returning to clobber 1 or 9 in the starting cell. In trying to get the AIC to come back to r2c1, can I use branch off winks for a slink got back to the start to close a nice loop? No, that logic is truly circular, and wrong in this case.
The branch winks are valid only if 6r2c1 is false, just as complex 1-way removals are. They work only because they are alternative to the starter candidate being true. We can’t use t branch winks in AIC to make any other conclusions.
That was the hard part. Now with NW6, we get two simple 1-ways.
Adding color, a third simple 1-way wraps blue.
After
and follow up SEc7 boxline removals, a naked pair removes 3, and a 4 – cell remote pair piles on.
The red/orange expansion brings a 183-wing.
The expansion traps 1r6c2 and allows a shortcut ANL.
The 2r8c3 removal expansion traps 2r1c5, confirming S5, then N7.
We get a unique rectangle , where 1r2c3 => 4r2c2 and 1r9c2 => 4r9c3,
but the closing curtain is the slink AIC joining red 1’s. Yes, orange 1 sees them both and one of them must be true, but beyond that, they’re red. If one is true, both are true. And yes, Virginia, ANL terminals can both be true.
The orange wrap collapses KDI 475.
Next week, we have the two recent (in my paper) Dave Green Sunday 5-stars below.
By my reckoning one barely gets through line marking and one almost does. I have them on the last post before the pause, because of their 4-fills. This week, see if you agree.
Systematic Sudoku 