dailysudoku.com

[Earl]

289xywing @R3C3, -9R2C3

Early Earl

PS I spoke too soon. I agree with Don. I needed 689xywing and 268xyzwing to solve it. Thanks Don.

[dongrave]

After basics:

[TomC]

[dongrave]

Note: I have replaced the less than sign immediately followed by the greater than sign in many places below with the text 'is not' due to an apparent bug that screws up the text when posting.

Nice solution Tom! Of course there are a lot of ways to represent your solution. Your solution can be expressed as a typical 'simple coloring' solution involving 5 cells that all include the candidate 6.

When I read the solution exactly as you've described, I read it as follows:
If r6c9 = 6, then r8c9 is not 6 and r6c6 is not 6 so r9c6 = 6 so r9c8 is not 6 so there's no 6 in box 9; so r6c9 is not 6.

But you could instead assume that r6c9 is 6 and reach a contradiction as follows: If r6c9 = 6, then r6c6 is not 6 so r9c6 = 6 so r9c8 is not 6 so r8c9 = 6 contradiction, so r6c9 is not 6.
(The Eureka notation for this would be: 6r6c9 - r6c6 = r9c6 - r9c8 = r8c9 contradiction => r6c9 is not 6.)

But even a little nicer than a chain with a contradiction would be a forcing chain with pincers on both ends. I learned this from Marty and Clement a few years ago and the logic goes as follows:
If r6c6 = 6 then r6c9 is certainly not 6 and if r6c6 is not 6 then I can show you that r8c9 = 6 so either way r6c9 is not 6.
(The Eureka notation for this would be: 6r6c6 = r9c6 - r9c8 = r8c9 => r6c9 is not 6.)

[TomC]

Thanks, notation for me has always been difficult, but this helps a lot.

[ZeroAssoluto]

Hi everyone,

W-Wing 5,6 in r2c1,r9c8 SL with number 5 in r8c19 and -6 in r2c8
or
Skyscraper with number 6 in r69c6,r68c9 and -6 in r8c5,r9c8
or
2 String Kite with number 6 in r9c68,r68c9 and -6 in r6c6
or
2 String Kite with number 6 in r69c6,r8c59 and -6 in r6c9

Ciao Gianni