A variety of Sudoku Variants

For fans of Killer Sudoku, Samurai Sudoku and other variants

A variety of Sudoku Variants

Postby tso » Sun Jul 24, 2005 5:24 am

These images are also here:
http://sudokuvariants.blogspot.com/ ]


The names are merely descriptive. I don't know what they may actually be named. They are all from Japanese magazines 5 to 10 years old.

Image
Irregular groups.
Very common variant. Sub-groups are irregular instead of 3x3 boxes. These irregular groups may or may not be symmetrical.

Image
Disjoint groups

In addition to the standard 27 groups (rows, columns, boxes), there are 9 more "disjoint" groups, each shaded on of 9 colors. All digits on one color must be different.

Image
Diagonals

The two main diagonals must also contain each digit.

Image
Extra groups

In addition to the standard 27 groups (rows, columns, boxes), there are 4 more groups, shown with shading. The number of auxillary groups varies.

Image
Even and Odd

Dark shaded cells will have even numbers, light will have odd.

Image
Overlapping plus diagonal groups

These overlapping puzzles include diagonal groups -- the 4 main diagonals must have one of each digit.

Image
Overlapping

A variation from the standard overlapping puzzle


Image
Overlapping
A variation from the standard overlapping puzzle. Cells marked with squares are not used in solving, only for sending in solution. Purpose for STAR cell is unknow. I'm guessing it's a hint -- either something like START HERE -- or possible there is an actual clue somewhere in the magazine. I don't know; I don't speak Japanese.


Image
Three overlapping -- tight


Image
Four Overlapping, standard
Again, don't know what the star is for. You can ignore the four square marks in cells.
Image
Four overlapping variation

A variation of the standard 4 overlapping puzzle

Image
Five overlapping, standard


Image
Seventeen overlapping 9x9 puzzles

Image
25x25
Notice the English word TEN is embedded in the pattern and it's not quite symmetrcial.
Last edited by tso on Sun Jul 24, 2005 4:58 pm, edited 1 time in total.
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Postby tso » Thu Aug 11, 2005 12:35 am

I've edited the previous post in the hopes that the images will now display properly. PM me if the do not, otherwise, reply here.
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Postby lunababy_moonchild » Thu Aug 11, 2005 6:56 am

I've seen the Irregular Groups, and the Diagonals but nothing else.

Certainly are interesting variations to the standard 9 x 9 puzzle.

Luna
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Postby The Druid » Thu Aug 11, 2005 5:51 pm

I can see them all correctly. How exciting they are! Thanks, Tso, for posting them.

The Druid
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Postby tso » Fri Aug 12, 2005 8:08 pm

This puzzle is in the PQRST 14 competition. (Puzzle number 4).

Fill the grid with the digits 1 - 7, so that no two digits are in the same row or column. The clues give are the products of the four cells that meet at that corner. (The puzzle isn't quite a Sudoko variant as there are no boxes, just rows and columns, so it's more of a Latin Square variant.)

Code: Select all
+-----+-----+-----+-----+-----+-----+-----+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+-----+-----+-----+---[168]---+----[ 24]--+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+-----+-----+---[120]---+-----+-----+-----+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+---[192]---+---[ 60]---+---[105]---+-----+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+-----+-----+-----+---[120]---+-----+-----+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+---[ 36]---+-----+-----+-----+-----+-----+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+-----+---[ 20]---+---[ 84]---+-----+-----+
|     |     |     |     |     |     |     |
|     |     |     |     |     |     |     |
+-----+-----+-----+-----+-----+-----+-----+
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Postby tso » Fri Aug 12, 2005 8:12 pm

Menneske has started to make irregular-group puzzles, like the one at the very top of this thread.
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Postby tso » Sat Aug 20, 2005 2:01 am

Menneske has started to make Sudokus with Diagonals.
and Disjoint Groups. Disjoint Group Sudoku, until now, have been rarely found outside if Japanese Puzzle magazines.
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Postby dukuso » Sat Aug 20, 2005 5:59 am

can you also make another thread without the pictures,
just the descriptions ?
It's loading slowly with the pictures.
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Postby Lardarse » Mon Aug 22, 2005 1:20 pm

Has anyone tried the Sum Doku that is also listed on the linked page? I'm trying to do it and it's bloody hard...
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Postby tso » Mon Aug 22, 2005 3:17 pm

Hmm ... looks like I left these three out of the original post:

SUM DOKU
Image

Clues are the sum of several cells.
EDIT: IMPORTANT! No digit may appear twice within any of the numbered areas marked by dotted lines.

I've also seen these where the PRODUCT is used instead of the SUM.

SEQUENTIAL PUZZLE

Image

Seqential puzzle.
Must be solved in sequence. Start with upper right, then follow arrows. After solving first puzzle, transfer six numbers in to the cells marked with squares in the second puzzle, etc. Solver may have to work in both directions. Topologicly, this is the same concept as the overlapping puzzles, but in this case, the overlap is disjoint cells. Any cell marked with a square in puzzle X is really one and the same cell in puzzle X-1.


DIAGONALS, NO BOXES

Image

Diagonals, no boxes.
This is a primative variation. Groups are rows, columns and two main diagonals -- no boxes.
Last edited by tso on Wed Aug 31, 2005 9:14 pm, edited 1 time in total.
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Postby Moschopulus » Mon Aug 22, 2005 11:24 pm

I don't think you mentioned this variant:
http://www.mathpuzzle.com

Some squares are coloured blue.
For each number k from 1 to 9 there is a box with k blue squares.
In the box with k blue squares, the numbers from 1 to k must go
in the blue squares.
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Postby tso » Thu Aug 25, 2005 3:25 pm

This is the puzzle from Mathpuzzle.com

Each row, column, box and the two main diagonals contain 1 of each digit.

Also, each cell marked with an 'o' contains a smaller digit than the starting digit in the same box.

Code: Select all
 . . . | o 7 o | . 6 o 
 . . . | o . o | o o o 
 2 o . | o o . | . . o 
-------+-------+-------
 o o o | o o . | . . . 
 o 9 o | . 5 o | . . . 
 o o o | . . o | 1 . . 
-------+-------+-------
 o . 4 | . . . | o o o 
 . o o | . . . | o o o 
 . . . | o o 3 | 8 o .
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Postby catilina » Thu Aug 25, 2005 8:52 pm

I have tried the (invalid?) Sum Doku and found 3 (?) solutions.

Code: Select all
(1)

+-------+-------+-------+
| 6 8 9 | 3 7 2 | 1 4 5 |
| 4 1 2 | 5 8 9 | 6 7 3 |
| 5 3 7 | 4 6 1 | 9 8 2 |
+-------+-------+-------+
| 1 2 4 | 9 5 7 | 3 6 8 |
| 7 9 3 | 8 2 6 | 4 5 1 |
| 8 5 6 | 1 3 4 | 7 2 9 |
+-------+-------+-------+
| 3 6 1 | 2 4 8 | 5 9 7 |
| 2 4 5 | 7 9 3 | 8 1 6 |
| 9 7 8 | 6 1 5 | 2 3 4 |
+-------+-------+-------+

(2)

+-------+-------+-------+
| 6 8 9 | 3 7 2 | 1 4 5 |
| 4 1 2 | 5 8 9 | 6 7 3 |
| 5 3 7 | 4 6 1 | 9 8 2 |
+-------+-------+-------+
| 1 2 4 | 9 5 7 | 3 6 8 |
| 9 7 3 | 8 2 6 | 4 5 1 |
| 8 5 6 | 1 3 4 | 7 2 9 |
+-------+-------+-------+
| 3 6 1 | 2 4 8 | 5 9 7 |
| 2 4 5 | 7 9 3 | 8 1 6 |
| 7 9 8 | 6 1 5 | 2 3 4 |
+-------+-------+-------+

(3)

+-------+-------+-------+
| 6 8 9 | 3 7 2 | 4 1 5 |
| 4 1 2 | 5 8 9 | 7 6 3 |
| 5 3 7 | 4 6 1 | 8 9 2 |
+-------+-------+-------+
| 1 2 6 | 9 5 7 | 3 4 8 |
| 9 5 3 | 8 2 4 | 6 7 1 |
| 8 7 4 | 1 3 6 | 5 2 9 |
+-------+-------+-------+
| 3 6 1 | 2 4 8 | 9 5 7 |
| 2 4 5 | 7 9 3 | 1 8 6 |
| 7 9 8 | 6 1 5 | 2 3 4 |
+-------+-------+-------+


I liked this one, though. Does anybody know a source for these "Sum Dokus"?
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Postby tso » Fri Aug 26, 2005 3:16 am

Too bad it has multiple solutions. It's hand made from a old Japanese magazine. (I don't speak Japanese -- there may have been an additional verbal clue.) I don't know of any regular source. That was one of the reasons I made this post -- to get some people interested in creating some of the different variations. And it's worked, as Vegard Hanssen is now make several of the best variants here.

I'll check my stacks for other Sum Duko.

Edit: Only last solution is valid. First two have duplication of digits in one enclosure. r7c5-r7c6-r6c6-r6c7 cannot be 4-8-4-7 as it is in the first two -- it can only be 4-8-6-5 as it is in the last one.
Last edited by tso on Sun Sep 04, 2005 2:33 am, edited 1 time in total.
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Postby Lardarse » Fri Aug 26, 2005 11:53 am

Are those teh only solutions that fit? Because I found that a 4 in R3C4 leads to a contradiction...

LA

Edit: That's only becase I then somehow managed to put a 3 in R3C9...
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