dailysudoku.com

[ZeroAssoluto]

Hi everyone,

[TomC]

Since I learnt that the VH puzzles can be solved with X,XY or XYZ that's what I try to look for, maybe not so successfully.

What I saw was r8c8 <> 6 as then r89c7 = 14 and r1c8= 4 leading to no 4's in box 6

[Mogulmeister]

That's a nice ANP, Tom (Almost Naked Pair) based around the <146> at r89c7.

Simply put - either the naked pair <14> is true or the "fin" 6 is true.

Whatever, there can be no 6 in r8c8.

Here's the forcing chain:

(6=14)r89c7-(4)r4c7=r4c8-(4=6)r1c8 ==> r8c8<> 6

[TomC]

Mogulmeister, thanks for letting me know what I'm doing!

Another way to solve could be r89c7 <>4 as then r4c7=7, r6c9=9 leads to only 2's in r89c9

[Mogulmeister]

...and that is your contradiction loop which is the same chain as above but extended one more step. The <> 6 in r8c8 creates a 249 triple (in red) which removes both the 4's at the start point!

(6=14)r89c7-(4)r4c7=r4c8-(4=6)r1c8-(6=49|249|249)r8c89,r9c9 ==>
r89c7<>4

[TomC]

I understand the forced chain of my first solution, but not sure about this explanation.

[Mogulmeister]

What I was doing Tom was extending your first forcing chain by a single step and creating the general contradiction loop. I was taking the line of least resistance from your former structure to get the same result. An extension of your original idea.

There are multiple contradictions that all create the eliminations of the two 4's. This stems from the fact that we have plugged 4 into the start at r89c7. These are all kicking off at once.

[Mogulmeister]

Your two:

(6=14)r89c7-(4=7)r4c7-(7=9)r6c9-(9=24|24)r89c9 ==> r89c7 < >4

(6=14)r89c7-(4=29|29)r89c9-(9=7)r6c9-(7=4)r4c7 ==> r89c7 < >4

[TomC]

Thanks, Mogulmeister this helps me move forward with sudoku (especially eureka, but I'm not there yet!)

Going back to my first solution (ANP) I thought this was also an XY chain with r1c8 and r8c7 being pincers on 6 which would remove the 6 in r12c7 and r8c8

On my second try you have turned this into two different solutions but to my mind it's only the direction that changes - clockwise or anticlockwise

iechyd da

[Mogulmeister]

Yes. An xy chain is traditionally a series of linked bivalues- only two candidates per cell. Hence the “xy”.



That’s just terminology.

However, as you said, the pincer idea is the most important one and how they are connected is what matters.

How did you link the 6s in r1c8 and r8c7 ?

[TomC]

My thought process was
if r1c8 = 6 then it eliminates
if r1c8 = 4 then r4c7=4, r9c7=1, r8c7=6
so either 6 is in r1c8 or r8c7

I didn't use the 79 in box 6 but if I did then maybe it is an XY chain

[Mogulmeister]

It’s only “a quasi xy” if you include the 79 in box 6 because of the tri value at r8c7. However, none of this matters a whole lot since the fundamental pincer op works via strong links and you don’t need the 79. All good.

The contradiction loop uses the same pathway but the direction of travel matters. Clockwise, the 4’s in r89c7 are eliminated via the <24> pair. Anti-clockwise the 4’s are eliminated by the 4n r4c7.

[Mogulmeister]

Did you see the mutant xy wing on steroids ?

Consider r4c7 - r6c9 - r89c9 as the mutant or double finned XY wing.

If r4c7 = 4 then it eliminates the 4s in r89c7.

If not then r4c7 = 7 and r6c9= 9 and r89c9 = locked pair <24> which eliminates the 4s in r89c7.

Eureka

(4=7)r4c7-(7=9)r6c9-(9=24|24)r89c9

r89c7 <> 4