Twins Construction Examples

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Twins Construction Examples

Postby Elzo Nguyen » Tue Sep 13, 2011 12:47 am

I use an example from Sudocue top10000 number 5 and HoDoKu program to simplify my work.
Thank you Sudocue and HoDoKu.

Sudocue-top10000 #05
Code: copy givens
...19.....1.....9.....3.8.1.6...493...5.8.1...945...8.9.3.4.....2.....7.....59...

After some moves of HoDoKu Techniques such as:
Locked Candidates Type 1, Naked Triple, Naked Single, Empty Rectangle, Finned Swordfish.
And before a Sue de Coq arrives.

Copy Candidates:
.----------------------.--------------------.---------------------.
| 2345678 34578 2678 | 1 9 25678 | 234567 2456 23467 |
| 2345678 1 2678 | 24678 267 25678 | 234567 9 23467 |
| 24567 457 9 | 2467 3 2567 | 8 2456 1 |
:----------------------+--------------------+---------------------:
| 1278 6 1278 | 27 127 4 | 9 3 5 |
| 237 37 5 | 9 8 2367 | 1 246 2467 |
| 1237 9 4 | 5 1267 12367 | 267 8 267 |
:----------------------+--------------------+---------------------:
| 9 578 3 | 2678 4 12678 | 256 1256 268 |
| 45 2 168 | 3 16 168 | 345 7 9 |
| 14678 478 1678 | 23678 5 9 | 2346 1246 23468 |
'----------------------'--------------------'---------------------'

(see image in attachment)
U-Twins 1 from r9c8

Notice those three cells: r7c8 (red), r8c3 (blue) and r9c8 (blue).
If r9c8 is true, then r7c8 false and r8c3 true.
If r7c8 is true, then r8c3 and r9c8 false.

Coloring:
Cycle 1: blue
Cycle 2: red

Starting by cycle 1 (blue):
From r9c8 (cycle 1)
=> r7c8 (cycle 2) strong link with r9c8
=> r7c6 (cycle 1) strong link with r7c8
=> r8c3 (cycle 1) only cell in box 7 can be, because of r9c8
=> r4c3 (cycle 2) only cell outside box 7 on column 3 can be a hidden strong link for r8c3
=> r4c5 (cycle1) only cell outside box 4 on row 4 can be a hidden strong cell for r4c3
=> r6c1 (cycle 1) only cell in box 4 can be, because of r4c5
=> r9c1 (cycle 2) only cell outside box 4 on column 1 can be a hidden strong cell for r6c1.

Four cells r6c56 and r8c56, belonging to cycle 2 because of r4c5 (cycle 1) in box 5 and r7c6 (cycle 1) in box 8, make U-Twins.

This U-Twins belongs to cycle 2, so all cells of cycle 2 contain digit 1.
Cycle 2 (red) = 1

Conclusion: r4c3 = 1; r7c8 = 1 and r9c1 = 1.

After some basic moves, I come to the following grid.

Copy Candidates:
.-------------------.--------------------.--------------------.
| 34567 34578 278 | 1 9 2567 | 23467 2456 23467 |
| 34567 1 27 | 24678 267 25678 | 23467 9 23467 |
| 4567 457 9 | 2467 3 2567 | 8 2456 1 |
:-------------------+--------------------+--------------------:
| 8 6 1 | 27 27 4 | 9 3 5 |
| 237 37 5 | 9 8 2367 | 1 246 2467 |
| 237 9 4 | 5 1267 12367 | 267 8 267 |
:-------------------+--------------------+--------------------:
| 9 578 3 | 2678 4 2678 | 256 1 268 |
| 45 2 68 | 3 16 168 | 45 7 9 |
| 1 478 678 | 2678 5 9 | 2346 246 23468 |
'-------------------'--------------------'--------------------'




(see image from attachment)
L-Twins 5 starting from r1c2

Starting by cycle 1 (blue)
From r1c2 (cycle 1)
=> r7c2 (cycle 2) only cell outside box 1 in column 2
=> r8c1 (cycle 1) strong link with r7c2
=> r8c7 (cycle 2) strong link with r8c1
=> r7c7 (cycle 1) strong link with r8c7
=> r3c8 (cycle 1) only cell in box 3 can be, because of r1c2
=> r1c8 (cycle 2) strong link with r3c8
=> r2c6 (cycle 1) only cell in box 2 can be, because of r1c2 and r3c8
=> r3c6 (cycle 2) only cell in box 2 can be, because of r1c8 and r2c6
=> r2c1 (cycle 2) only cell in box 1 can be, because of r1c8 and r3c6.

(see image from attachment)
L-Twins 5 starting from r3c2

Starting from r3c2 (cycle 1) (blue), I can finish Twins in every boxes. Twins do not change their cells, even though two cells change from cycle to cycle and one cell changes because the starting cell changes of course. See image above.

Note:Twins change only in boxes 1 and 2.

This is Locked – Twins in column 2, cells r13c2, so cell r7c2 ( only cell outside box 1 on column 2) does not contain candidate.

Therefore r8c1 = 5 => r7c7 = 5 => r2c6 = 5, because r1c28 and r3c28 become X-Wing.

Finally, the game needs simple techniques such as locked candidates and single digit to solve.

The game is solved.
Attachments
Twins Construction Example.pdf
(108.62 KiB) Downloaded 94 times
Elzo Nguyen
 
Posts: 8
Joined: 11 September 2011

Re: Twins Construction Examples

Postby ronk » Tue Sep 13, 2011 1:51 am

Elzo Nguyen, you now have the notion of "Twins" and how it can be presumably be used to solve puzzles in five ... not one, not two, not three, not four ... but five different threads. I remind you that no one else thinks you have a valid technique. Moreover, I and eleven have explicitly stated that the idea yields invalid results and uses invalid 'links' or 'inferences.'

So please limit your conjecture to one thread until there is corroboration, naye until there is proof, that your technique is valid.

BTW there is provision on this forum to post links to images on other sites, sites such as tinypic.com, imageshack.com or any other image hosting site including your own.

BTW2 I'm still mulling it over, but I may merge all your 'Twins' posts (up to and including the one above) into one thread.
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Re: Twins Construction Examples

Postby Elzo Nguyen » Tue Sep 13, 2011 8:41 am

Thank you ronk and eleven for replies.
Neither I think that Twins is valid. It is just a lucky move.
So I stop all my works here to annoy no body.
I apology for that.
Elzo Nguyen
 
Posts: 8
Joined: 11 September 2011


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