Finned X-Wing With Empty Rectangle

Advanced methods and approaches for solving Sudoku puzzles

Finned X-Wing With Empty Rectangle

Postby civiliza » Fri Aug 02, 2013 10:00 am

Having recently implemented Empty Rectangles in my generator, I have just realised that in certain situations, an Empty Rectangle can be combined with a Finned X-Wing to form a double elimination.

Given the single digit pattern:
Code: Select all
 d d d | . c . | . . .
 . . 5 | . 5 . | . . .
 d d d | . c . | . . .
-----------------------
 . . . | . c . | . . .
 . . . | . c . | . . .
 . . . | . c . | . . .
-----------------------
 a a 5 | . 5 . | . . .
 . . b | . c . | . . .
 . . b | . c . | . . .


When there is a 5 in one or more of each of the a, b, c, and d cells, then there is both a finned X-Wing in r27c35 and an Empty Rectangle in square/block 7 combined with a strong link in r2c35.

The finned X-Wing would eliminate 5 from the b cells and destroy the Empty Rectangle, while the Empty Rectangle would eliminate the 5 in r7c5 and destroy the finned X-Wing. When done at the same time though, it should logically be possible to eliminate the digit 5 from both r7c5 and the b cells.

(I have no idea how often this pattern would occur, but it has made me think twice about whether I want to implement Finned X-Wings)

EDIT - The c and d cells are just there to avoid other types of eliminations, what I was interested in was the Finned X-Wing in r27c35 combined with the Empty Rectangle in square/block 7.
civiliza
 
Posts: 64
Joined: 25 October 2010

Re: Finned X-Wing With Empty Rectangle

Postby Sudtyro2 » Fri Aug 02, 2013 6:38 pm

With the b's eliminated, by whatever method, there remains a truth only in b7's r7c123, which then immediately kills (5)r7c5.

BTW, a finned X-Wing will eliminate the b's, but I prefer a simple AIC:
Code: Select all
(5): r7c123=r7c5-r2c5=r2c3 => r89c3<>5
Sudtyro2
 
Posts: 464
Joined: 15 April 2013

Re: Finned X-Wing With Empty Rectangle

Postby civiliza » Fri Aug 02, 2013 7:19 pm

Sudtyro2 wrote:With the b's eliminated, by whatever method, there remains a truth only in b7's r7c123, which then immediately kills (5)r7c5.


D'oh, you are right of course - by pointing r7c123 clears out the 5's from the rest of row 7.
civiliza
 
Posts: 64
Joined: 25 October 2010

Re: Finned X-Wing With Empty Rectangle

Postby Sudtyro2 » Sat Aug 03, 2013 1:16 pm

civiliza wrote: -- it should logically be possible to eliminate the digit 5 from both r7c5 and the b cells.


FWIW, I overlooked the fact that either of your two methods alone will eliminate both r7c5 and the b cells. I.e., I hadn't checked the Empty Rectangle approach that first eliminates r7c5, thus forcing a truth to reside in r7c123, which then kills the b's in b7. So, your basic premise was intuitively correct...but you only need one method to do both eliminations.
Sudtyro2
 
Posts: 464
Joined: 15 April 2013

Re: Finned X-Wing With Empty Rectangle

Postby civiliza » Mon Aug 05, 2013 12:17 pm

Sudtyro2 wrote:I hadn't checked the Empty Rectangle approach that first eliminates r7c5, thus forcing a truth to reside in r7c123, which then kills the b's in b7. So, your basic premise was intuitively correct...but you only need one method to do both eliminations.


Once again "d'oh", having become overly obsessed with Empty Rectangles, I was used to them only eliminating one cell of many in a house (in this case row 7). I hadn't realised that the pre-requisites of the Finned X-Wing meant that it was the only such cell outside of Block 7.

So the Finned X-Wing eliminates the b cells, after which pointing eliminates r7c5; while the Empty Rectangle eliminates r7c5 after which claiming eliminates the b cells.

Thanks for clarifying my muddy thinking Sudtyro2, I could see the two techniques interfering with each other, but failed to realise they led to the same elimination(s) in the long run.
civiliza
 
Posts: 64
Joined: 25 October 2010


Return to Advanced solving techniques