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  • Hacker News
  • I’ll plug a 4x4 variant sudoku generator that Claude put together a few months ago.

    https://yakymp.github.io/sudoku4x4/

    by cochleari_major
  • In addition to the (n^2)^2 sudokus, you can also make them with rectangular sub-blocks -- (n x m) ^ 2 sudokus -- such as a 6x6 grid with six (3x2) sub-blocks, or a 10x10 with 10 5x2 sub-blocks.
    by Polizeiposaune
  • That's interesting, less than I thought. I'm curious about this because I'm working on a sudoku variant that has two pieces of data in each cell - such as numbers and letters. I am keen to try out your process with that arrangement.
    by _usefulcat
  • I love articles where a seemingly simple puzzle turns out to be much more interesting when you look at it from the perspective of math and code. It’s especially interesting to learn that there aren’t actually that many possible 4×4 Sudoku grids. I also enjoy working with puzzles and creating my own crosswords in SuperColoring. Articles like this make me want to try creating a more unusual crossword and see how much harder it would be to solve.
    by irusik
  • I'm glad this inspired something in you!
    by Fran314
  • Here is one possible way of generating all 12 solutions by 2x2x3 choices:

    1. Fill the upper left box with 1-2-3-4

    2. Choose where to put the 1 in the top right box (2 choices)

    3. Choose where to put the 1 in the lower left box (2 choices)

    4. Choose which digit to put diagonally opposite the 1 in the lower right box (3 choices)

    Is there a nicer way which makes it obvious that there is exactly one solution for each choice in the last step?

    by antonTobi
  • > Choose which digit to put diagonally opposite the 1 in the lower right box (3 choices)

    There are only two choices there. You cannot put a 1, nor the digit (3 or 4) that’s in the top the column where you try to put the number.

    > Is there a nicer way which makes it obvious that there is exactly one solution for each choice in the last step?

    There isn’t. You may end up with a degree of freedom after step 4

      1234    1234
  ..1.    ..1.
  ...1    ...1
  .1..    .14.
    leads to

      1234
  ..12
  ..21
  2143
    which allows for 2 solutions:

      1234    1234
  3412    4312
  4321    3421
  2143    2143
    by Someone
  • This looks related to https://oeis.org/A107739.

    If the 4x4 sudoku has 288 / 4! = 12 distinct solutions, then does the 9x9 sudoku have 6670903752021072936960 / 9! distinct solutions?

    by drmajormccheese
  • Or, for the unique solutions: https://oeis.org/A285180
    by alright2565
  • There is a way of understanding all this through group theory. eg:

    https://arxiv.org/html/2607.20669

    'Counting, Symmetries and Equivalence Classes of Sudoku Grids' where an 'equivalence class' is a set of structures (such as filled Sudoku grids) that are all equivalent under some relation.

    by gilleain
  • Can't you just describe the group that defines those transformations and use Burnside?
    by qsort
  • In the last few days I went down the rabbithole of 4x4 sudokus, and found out that (up to permutations) there are only 12 possible solutions.

    I decide to write up the small research I did as well as some fun findings discovered along the way in a blog post.

    Also, yes this is extremely pointless and silly, and the math involved is not incredibly high level, but I still think it's an enjoyable bit of recreational math worth your time!

    by Fran314
  • Did you check for rotational and mirror symmetry? As in, are the 12 unique sudokus just the same one, rotated in 4 ways, and mirrored along the x or y axis?
    by redfast00