How many possible 2x2 soduku's?

JPF · Posted: Sat Mar 29, 2008 5:49 pm Post subject:

I hope I'm right*.

There are 36 non isomorphic minimal puzzles :

4 clues : 13 puzzles

tpgames · Posted: Sun Mar 30, 2008 11:53 pm Post subject:

Fascinating! I'm going to look at your data and the other links in June, when I finally have the time and try once more to write that sudoku game. Currently, I'm using someone else's code with permission thats a 9x9 grid. The code does not give you authentically unique sudokus games, but it works good enough for me. I'm beginning to understand JS better. So, June should be doable. I'll post some of the code if I ever figure it out. Laughing

It will be for the 2x2 sudoku game, with images.

mathrec · Posted: Tue Apr 01, 2008 11:09 pm Post subject: Minimal 2x2

I got the same 36 minimal puzzles that you did. My results were generated separately by hand and by computer and they match with yours, so I'm pretty sure that 36 is the correct total.

Here's my list of all 36, sorted according to the arrangement of clues:

Four clues all different in four boxes:
4: 1.2.....3..4....
4: 1.2......3.4....
4: 1.2......3.....4
4: 1.....2..3.....4
Four clues all different in three boxes:
4: 12......3.4.....
4: 1.2..3.....4....
Four clues with one value clued twice in adjacent boxes:
4: 12......2.....3.
4: 1.2......1.3....
4: 1.....1..2.....3
Four clues with one value clued twice in diagonal boxes:
4: 1.2......2.3....
4: 12......3.....1.
4: 12........13....
4: 1.2..3....1.....
Five clues with one value clued twice in adjacent boxes:
5: 1.2..2....3....4
Five clues with one value clued twice in diagonal boxes:
5: 12..3.....1....4
5: 12..3.....2....4
5: 12......3.1...4.
5: 12......3.2....4
5: 1.2..3...24.....
Five clues with two values clued twice in the same adjacent boxes:
Five clues with two values clued twice in overlapping adjacent boxes:
5: 1.2..2.3.1......
5: 1.2..2...1.....3
Five clues with two values clued twice in nonoverlapping adjacent boxes:
5: 1.2..2..3.....3.
Five clues with two values clued twice in the same diagonal boxes:
5: 12..3.....1....2
5: 12..3.....2....3
5: 1.2..3....3....1
Five clues with two values clued twice in different diagonal boxes:
5: 123.....3.1.....
5: 123.....3.2.....
Five clues with two values clued twice in adjacent and diagonal boxes:
5: 123.....23......
5: 123.3.....1.....
5: 123.....2.1.....
5: 12......3.1....3
5: 12......3.2....3
5: 1.2..2.33.......
5: 1.2..2..3.....1.
5: 1.2..2....3....1
Six clues:
6: 12......2.3..31.

The same script that I wrote to determine the number of minimal puzzles also found the total number of distinct (non-isomorphic) puzzles: 4708 (not including underdetermined configurations or the two full-board configurations).

mrmarky2 · Posted: Tue May 13, 2008 2:56 pm Post subject:

JPF · Posted: Wed May 14, 2008 5:02 pm Post subject:

Frazer's explanation is clear.

If it's useful, here's one considering the rows :
First row : 4! = 24 possibilities
Here's one :

coloin · Posted: Thu May 15, 2008 6:02 pm Post subject:

Well this was a good question Exclamation

It was my first ever forum post, a long time ago - I thought there were 192......on paper.

There are 4+2 = 6 ways to compete the grid in JPFs example above.

tannedblondbloke here - he got 192, which bugged me a bit.

But.....