SudoCue Users
A forum for users of the SudoCue programs and the services of SudoCue.Net

Author Message
keith
Hooked

Joined: 07 Feb 2006
Posts: 35
Location: near Detroit, Michigan, USA

Posted: Mon Apr 03, 2006 9:05 pm    Post subject: April 3, 2006: Type 6 Unique Rectangle

Today's Nightmare has an example of what Ruud has suggested should be a "Type 6 Unique Rectangle".

http://www.sudoku.com/forums/viewtopic.php?t=3709

I have suggested the name "Unique X-wing", in a different Forum.

After making the elementary reductions you get to:

 Code: +----------------+----------------+----------------+ | 356  2    56   | 8    7    1    | 9    35   4    | | 1358 4    58   | 69   69   2    | 35   18   7    | | 18   9    7    | 45   3    45   | 6    128  28   | +----------------+----------------+----------------+ | 258  58   9    | 25   1    7    | 4    6    3    | | 256  1    3    | 2569 4    59   | 8    7    259  | | 4    7    256  | 3    69   8    | 1    25   259  | +----------------+----------------+----------------+ | 578  58   1    | 49   2    49   | 357  358  6    | | 9    6    258  | 7    58   3    | 25   4    1    | | 27   3    4    | 1    58   6    | 27   9    58   | +----------------+----------------+----------------+

How to find it:

1. There is a rectangle defined by a diagonal pair.
2. The rectangle is an X-wing.
3. The rectangle is potentially non-unique.

Then what? Well, the diagonal pair must be the same value as the X-wing.

The diagonal pair is <18> in R23C18. The X-wing is on <1>, the non-unique pattern is, of course, <18>. So, R2C8 and R3C1 must be <1>.

The proof is simple: If either of the diagonal pair is <8>, there is a non-unique rectangle through a forcing loop on <1>.

In this case, placing the <1>'s is not much help in solving the puzzle. (To progress, look at the rectangle in R47C12.)

Best wishes,

Keith
David Bryant
Gold Member

Joined: 20 Jan 2006
Posts: 86

 Posted: Mon Apr 03, 2006 11:41 pm    Post subject: DIC's will do it too Hi, Keith! From the position you posted two "doble-implication chains" will crack it wide open. The first is alpha star at r2c3: r2c3 = 8 ==> r2c8 = 1 r2c3 <> 8 ==> r8c3 = 8 ==> r9c5 = 8 ==> r7c8 = 8 ==> r2c8 = 1 Interestingly, this permits the same conclusion as your "unique x-wing." The second DIC is alpha star at r2c7: r2c7 = 3 ==> r7c8 = 3 ==> r9c9 = 8 r2c7 = 5 ==> r2c3 = 8 ==> {2, 5} pair in row 8 ==> r8c5 = 8 ==> r9c5 = 5 ==> r9c9 = 8 r9c9 = 8 is enough to crack it wide open. dcb
keith
Hooked

Joined: 07 Feb 2006
Posts: 35
Location: near Detroit, Michigan, USA

Posted: Sun Apr 09, 2006 4:26 am    Post subject: Update

I said:

 Quote: In this case, placing the <1>'s is not much help in solving the puzzle.

which I withdraw.

There are a number of ways to use chains to solve this puzzle. As with David's solution, the Unique Rectangle replaces the deduction made using a chain.

Replace "not much use" with "just one step".

Keith
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum SudoCue - the Website----------------Daily Sudoku Nightmare & ArchiveClueless SpecialsClueless ExplosionsWeekly AssassinsTexas Jigsaw KillersSudoku LiteX-FilesDaily WindokuDaily Jigsaw SudokuSolving Guide & GlossarySamurai ContestGeneral Website Comments Sudoku - the Community----------------Help Me! I'm stuck!Solving Techniques & TipsWebsitesSoftwarePuzzlesPublicationsOff-Topic SudoCue - the Software----------------SupportWishlistCommentsReleases
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum