Twin Equivalent Sudokus

aman · Posted: Sun Nov 19, 2006 8:45 pm Post subject: Twin Equivalent Sudokus

I have devised a new Sudoku variant called "Twin Equivalent Sudokus". It can be downloaded from the Yahoogroup Sudokuworld site http://games.groups.yahoo.com/group/sudokuworld/.

If you are not a member of Sudokuworld, please click on the button "Join This Group!" as member to access the file.

If you are already a member of Sudokuworld, please sign in by clicking the button "Sign in to Yahoo!". After that, you can download the file "Twin Equivalent Sudokus" from the folder "Equivalent Sudokus" under the file section.

Your comments are most welcomed Laughing

Ruud · Site Admin

Maybe you should post your puzzles directly on this forum, instead of forcing everybody to join a Yahoo group where Locked Candidates (by any other name) is considered one of the most advanced solving techniques.

Just post your puzzles in text format like this:

aman · Posted: Mon Nov 20, 2006 6:06 am Post subject:

Thank you, Ruud, for your helpful suggestion. I don't have any special connection with Sudokuworld although the group's leader Frank Vedel should be happy with me for providing a free service in "forcing everybody to join" his group.

The text format is good enough for posting standard Sudoku puzzles on the forum. However, it certainly cannot be used for posting other more complicated or "exotic" puzzles such as jigsaw puzzles.

I would be most thankful if you (or anybody else) could advise me on how to post such wonderful graphics directly onto the forum. Very Happy

Ruud · Site Admin

aman · Posted: Mon Nov 20, 2006 11:37 pm Post subject:

Ruud, thank you again for your help. I wonder whether the use of ImageShack's image hosting service is limited to this forum for setbb.com users. In other words, can I post any complicated image on other forums or websites?

As a precaution against any inconvenience caused to readers during the ImageShack® website's maintenance services, I try to avoid using its hosting service as much as possible except for the posting of complicated puzzles. Hence in this thread, I shall post my puzzles in the text format as suggested by you in your previous message.

Twin A

aman · Posted: Fri Nov 24, 2006 6:11 pm Post subject:

Here is another example for those who like to solve this type of twin puzzles.

Twin A

Twin B

"Twin Equivalent Sudokus" devised by Henry Kwok on 24th Nov 2006 Smile

aman · Posted: Fri Dec 29, 2006 1:29 pm Post subject:

A simple pair of linked puzzles by the name of "Twin Equivalent Sudokus" has been published on Dr Sam Guo's website http://www.chinasudoku.com/.

Click on the "Home" section if you cannot find the twin puzzles.

The twin puzzles, which are the first in the world to make use of stamp images, are designed by Henry Kwok. Approval to use the Singapore stamp images for the design and website display is given by the Infocomm Development Authority of Singapore and the Singapore Philatelic Museum (www.spm.org.sg), both of which are official agencies of the Government of Singapore.

Rules of Twin Equivalent Sudokus:

This sudoku variant consists of a pair of linked standard sudoku puzzles – one puzzle with some starting digits and the other puzzle with some members from a set of nine elements (Singapore stamp images). As usual, the object of this sudoku variant is to fill in the whole of the 9x9 grid with digits 1 through 9 or a set of nine elements (Singapore stamp images) so that each row, each column or each box contains all the digits 1 through 9 or nine elements (Singapore stamp images).

Both puzzles are essentially equivalent or the same puzzle. Twin B is related to twin A in the following ways:

Given that twin A is the original puzzle, twin B is obtained

1. By exchanging a block of columns (rows) with another block of columns (rows) in the original puzzle;

2. By rearranging all the digits 1 through 9 or nine elements (Singapore stamp images) so that each digit in twin A corresponds one to one to an element (Singapore stamp image) in twin B. Very Happy

holdout · Posted: Sun Dec 31, 2006 1:24 am Post subject: Equivalen Twins?

To: aman

How can your posted "Twin A" be equivalent to "Twin B" when they have a different number of filled cells?

aman · Posted: Sun Dec 31, 2006 4:56 am Post subject:

Welcome to my "parlour", holdout. Your comments and suggestions are greatly appreciated.

The rules for the twin puzzles are similar to the rules for the first two puzzles posted in the thread "Twin Equivalent Sudokus" in the forum http://www.sudoku.com/. Every twin in that thread also has a different number of filled cells.

After you read and carefully study RW's method in solving the first two puzzles, you will have some idea about the equivalence of the puzzles. Very Happy

aman · Posted: Fri Nov 02, 2007 7:43 pm Post subject:

I have posted a simple form of twin equivalent Sudoku puzzles called "Twin Chute-swapping Sudoku" on the Nov 2007 NRICH website http://nrich.maths.org/public/viewer.php?obj_id=5870

Both Sudoku puzzles are essentially one and the same puzzle. Each twin can be created from the other by swapping a horizontal/vertical chute or band of blocks with another horizontal/vertical chute or band of blocks.

aman · Posted: Sat Dec 01, 2007 7:18 pm Post subject:

I have created another simple form of twin equivalent Sudoku puzzles called "Twin Line-swapping Sudoku" for the Dec 2007 NRICH web page http://nrich.maths.org/public/viewer.php?rss=1&obj_id=5907&part=index

Both Sudoku puzzles are essentially one and the same puzzle. Each twin puzzle can be created from the other by swapping the rows/columns within a horizontal/vertical chute of three blocks.

aman · Posted: Tue Jan 01, 2008 3:59 am Post subject:

My creation "Twin Equivalent Sudoku" is posted on the Jan 2008 NRICH website http://nrich.maths.org/public/viewer.php?rss=1&obj_id=5969&part=index