## 2-3-4 Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### 2-3-4 Sudoku

How about this one: Each row, column, and 3x3 contains two 2's, three 3's, and four 4's.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

There exist a similar variant, a 10 x 10 sudoku where 1 one, 2 two, 3 three and 4 fours.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

I thought of that, but then we'd have a jigsaw Sudoku, as well.

How about that? Instead of a 2-3-4 Sudoku, a 1-2-3-4 jigsaw Sudoku.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

They must not be jigsaws. In the variant I know 2 x 5 boxes are used as usual in 10 x 10 sudoku.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Pyrrhon wrote:They must not be jigsaws. In the variant I know 2 x 5 boxes are used as usual in 10 x 10 sudoku. ....

I find it unpleasant that each box would have as many as 5 elements in common with each of two rows (or columns). Jigsaw is better for 10 x 10, at least if it's designed so that there are never more than 4, and usually not more than 3, cells in common between boxes and rows (or boxes and columns).

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

The comprimise would be to use a standard 9x9 grid with 3x3 boxes, but one cell in each row, box and column is split into two, each of which will contain a digit. See:

http://www.sachsentext.de/en/sudoku09_1.htm
tso

Posts: 798
Joined: 22 June 2005

If we write down the set of necessary numbers in each row/column/whatever (for a normal Sudoku we have {1,2,3,4,5,6,7,8,9}) then I've seen the following:
- {1,1,1,2,2,2,3,3,3} [I made one like this]
- {1,2,3,4,5,6,7,8,9,0}, but each row/column/box is missing exactly one [saw it on the Yahoo group]
- {1,1,1,2,2,2,3,3,3,4,4,4,5,5,5}, with like digits not orthogonally adjacent
- {1,2,2,3,3,3,4,4,4,4}, with like digits not orthogonally adjacent
- {1,2,3,4,5,6,7,8,9,0}, with some cells having two digits [this is a very common one]

I do agree that jigsaws would be better for 10x10, which is really unfortunate, but gives a lot more freedom.
qqwref

Posts: 6
Joined: 21 May 2006

There are other variants with repitition out

- 1122334455 (2x5 boxes)
- 123456789123456789 (18x18 sudoku, and 9x9 boxes without repetition)
- 11223344 (without boxes)
- 111222333444 (without boxes)
- 123456000 (called sub-sudoku)
- 123456789000 (called black-cell handling, 0 are black cells and not adjacent)

Logical would also be

122333 in a 6x6 sudoku
Pyrrhon

Posts: 240
Joined: 26 April 2006

I wouldn't call black cell Sudoku {1,2,3,4,5,6,7,0,0} or {1,2,3,4,5,6,7,8,9,0,0,0} because it uses specific, different rules and you already know all the black squares. The goal isn't to figure out where everything (including the black squares) is with the clues given, so it isn't at all the same.

I'd like to try some of these other variants though. Could you upload an example?
qqwref

Posts: 6
Joined: 21 May 2006

The black cell must not been known. See this picture. The rules here: Each region, row, and column contains numbers 1-9 and three black cells. The black cells have to obey Japanese crossword rules: no two are orthogonally adjacent, and they can't divide the grid up into two regions.

There is a page with dayly changing sudoku variant puzzles where somedays you can find

- 11223344 (without boxes)
- 111222333444 (without boxes)
- 123456789123456789 (18x18 sudoku, and 9x9 boxes without repetition)

I plan to come with repitional variants on my own page in some days. For now there are only other variants.

By the way, what was described as variant seen in a yahoo group is equivalent with the 0-9 sudoku (in cases of 0-9 sudoku where no 2-number cell has 2 given digits).

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

The thread was about 2-3-4 sudoku. I'm giving now 3 examples. Every row, column and box contains two 2's, three 3's and four 4's. The puzzles can be solved only by logic (without nishio or coloring). The third is the easiest one.

Puzzle 1:

Puzzle 2:

Puzzle 3:
Pyrrhon

Posts: 240
Joined: 26 April 2006

What have I wrought?

My off-the-wall suggestion for a 2-3-4 Sudoku has resulted in three such actual puzzles -- quite good ones, by the way. I did manage to solve all three.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

I'm really interested to read how you solved them, because as I think, the techniques in sudoku with repititions are not so easy to spot as the same techniques to use in other variants.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Pyrrhon wrote:I'm really interested to read how you solved them ....

Well, in the first puzzle for example, we need a 3 and two 4's (no 2's) in the upper right box, but r1c7 cannot be a 3 because the top row is already saturated with 3's, so that cell must be a 4.

The rest of the top row then needs a 2 and two 4's (no 3's). But r1c1 cannot be a 4 because column 1 is already saturated with 4's, so that cell must be a 2.

Reasoning not much more complicated than the above led to filling in at least half of the cells. Then it was guess-and-check -- find a cell with only two possibilities, where one choice led to a longish chain of conclusions (is that called a "forcing chain" or something?). When it finally led to a contradiction, the remaining choice for that cell could be filled in.

Nothing fancy.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

Thank you, but guessing and exclusion steps are not necessary.
A problem with this sudoku variant is that many subset reductions are always possible. Moreover you get many strong links. If a number must occur in a line or box n times and you have it in n+1 candidate cells then you have between every pair of cells with this candidate a strong link (this is (n+1)n/2 strong links in this line or box). This leads frequently to turbot fishs, x-wings, ...

Pyrrhon
Last edited by Pyrrhon on Tue Jun 20, 2006 1:31 am, edited 1 time in total.
Pyrrhon

Posts: 240
Joined: 26 April 2006

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