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There is an example where it says that because rectangle has 1s and 5s, to avoid deadly pattern one of them can not be 5. Why can it not not be 2 or 7? There are plenty of 5s around as there are 2s and 7s. The example jumps to verdict very sharply without explanation. The only help article does not provide more clarity.

Premise


Verdict


The 5s are not the only ones on none of the rows of columns of the rectangle. Why R9C1?

Hi kurbads,

The key is that r7c6 is a bi-value cell.
If you were to put 5r9c1, you would force 1s in r7c1 and r9c6, which would in turn force 5r7c6, creating a UR.

Marek

My solver gets R9C1 <> 5 in a completely different manner.

When I was implementing ALS-xz, I couldn't understand how to efficiently pick the second set of cells, so I ended up using the interactions between a cell with two values and a whole line or box.

In this case R9C7 and box R7C1-R9C3.

If R9C7 = 5 then R9C1 <> 5.

If R9C7 = 7 then R7C1 = 7 and R9C1 = 1.

So in either case R9C1 isn't 5.

PS Even after this elimination my solver still needed a couple of XY-Chains and a W-Wing to solve it.

Interesting, that sounds more like a Grouped AIC (though it probably has a wing name Grouped H-Wing) than an ALS-XZ rule.
There is an ALS pattern that eliminates it: r9c7 and r789c2 r9c3, 7 is restricted common.

I think the easiest way to solve the puzzle is a different AIC of length 3, I believe this one is called H-Wing it's called M-Wing:
(2=4)r3c6 - 4r9c6 = (4-2)r9c2 = 2r2c2 => -2r2c6, -2r3c1; stte

Thanks jco for correct wing names.

well if we wish the easiest way to solve the puzzle
( not really what OP asked )
maybe "forcing nets"

5r9c1 would solve 1r9, 4c6, 2r3, 5r6c1, -5r9c1

About M-wings "M-Wings (by keith, Dec 2007)", and M-wing:
(x=y)-y=(y-x)=x.
The writing of it resembles the one for a W-wing
(x=y)-y=y-(y=x)
and M upside-down is W (though the reason for the letter M is "Medusa" colouring, as mentioned in the first reference).

Edit: improved text and added link.
Edit 2: improved text and removed unnecessary quote.