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ScienceQuiet 9d · day 10

Blog post enumerates 288 valid 4x4 sudoku solutions, 12 structurally distinct

Developer counts all possible 4x4 sudoku grids and puzzles using brute-force search and structural equivalence.

newest coverage 8d agosummary written 8d ago6 pieces64 likes & upvotes18 comments Hacker NewsLobstersMastodon

What to know

  • There are exactly 288 valid 4x4 sudoku solutions, but only 12 are structurally unique when digit relabeling is considered equivalent.
  • The post uses brute-force enumeration to count solutions and group them by structural equivalence under permutations.
  • The finding contrasts sharply with standard 9x9 sudoku, which has over 6.6 septillion possible solutions.

baldino Blog author

How it unfolded 3 developments, newest first · click a bar or a number to jump posts

Peak 2 pieces in 3h at Sep 14, 1 PM; 6 pieces over 10 days (4 posts · 2 comments) Sep 14, 7 AM — 1 piece · 1 post — Hacker News 1Sep 14, 10 AM — 1 piece · 1 post — Lobsters 1Sep 14, 1 PM — 2 pieces · 1 post · 1 comment — Lobsters 1, Hacker News 1Sep 14, 4 PM — 1 piece · 1 comment — Lobsters 1Sep 14, 7 PM — quietSep 14, 10 PM — quietSep 15, 1 AM — quietSep 15, 4 AM — quietSep 15, 7 AM — 1 piece · 1 post — Mastodon 1Sep 15, 10 AM — quietSep 15, 1 PM — quietSep 15, 4 PM — quietSep 15, 7 PM — quietSep 15, 10 PM — quietSep 16, 1 AM — quietSep 16, 4 AM — quietSep 16, 7 AM — quietSep 16, 10 AM — quietSep 16, 1 PM — quietSep 16, 4 PM — quietSep 16, 7 PM — quietSep 16, 10 PM — quietSep 17, 1 AM — quietSep 17, 4 AM — quietSep 17, 7 AM — quietSep 17, 10 AM — quietSep 17, 1 PM — quietSep 17, 4 PM — quietSep 17, 7 PM — quietSep 17, 10 PM — quietSep 18, 1 AM — quietSep 18, 4 AM — quietSep 18, 7 AM — quietSep 18, 10 AM — quietSep 18, 1 PM — quietSep 18, 4 PM — quietSep 18, 7 PM — quietSep 18, 10 PM — quietSep 19, 1 AM — quietSep 19, 4 AM — quietSep 19, 7 AM — quietSep 19, 10 AM — quietSep 19, 1 PM — quietSep 19, 4 PM — quietSep 19, 7 PM — quietSep 19, 10 PM — quietSep 20, 1 AM — quietSep 20, 4 AM — quietSep 20, 7 AM — quietSep 20, 10 AM — quietSep 20, 1 PM — quietSep 20, 4 PM — quietSep 20, 7 PM — quietSep 20, 10 PM — quietSep 21, 1 AM — quietSep 21, 4 AM — quietSep 21, 7 AM — quietSep 21, 10 AM — quietSep 21, 1 PM — quietSep 21, 4 PM — quietSep 21, 7 PM — quietSep 21, 10 PM — quietSep 22, 1 AM — quietSep 22, 4 AM — quietSep 22, 7 AM — quietSep 22, 10 AM — quietSep 22, 1 PM — quietSep 22, 4 PM — quietSep 22, 7 PM — quietSep 22, 10 PM — quietYesterday, 1 AM — quietYesterday, 4 AM — quietYesterday, 7 AM — quietYesterday, 10 AM — quietYesterday, 1 PM — quietYesterday, 4 PM — quietYesterday, 7 PM — quietYesterday, 10 PM — quietToday, 1 AM — quietToday, 4 AM — quiet 1–3
Sep 15Sep 16Sep 17Sep 18Sep 19Sep 20Sep 21Sep 22now · 6:44 AM ET
  1. 3

    Hacker News frontpage submission with expanded metrics

    A Hacker News post presents the findings with an updated title noting 85,632 possible puzzles alongside the 12 grid variants.

    • > An elegant way of finding the 12 solutions I found the 12 solutions by hand. If you label the four numbers in the upper-left big square 1, 2, 3, 4 by symmetry of permutations, then there's a second symmetry you can apply. The second symmetry is that swapping rows 3&4 or swapping columns 3&4 preserves whether a board is a solution. You can use…

      justinpombriocompsci,math,python9d ago4▲view on Lobsters ↗
    1 more of the top 2 · 2 posts in this stretch

    • I think B and C are identical (to symmetries) B B' C 1 2 4 3 3 4 2 1 1 2 4 3 3 4 2 1 1 2 4 3 3 4 2 1 4 3 1 2 2 1 3 4 2 3 1 4 2 1 3 4 4 3 1 2 4 1 3 2 B' is a label permutation of B: 1->3, 2->4, 3->1, 4->2. C is swapping the first 2 rows of B'. So they're equivalent. I used symmetry tricks over here https://hachyderm.io/@bazzargh/116286733347456470…

      bazzarghcompsci,math,python9d ago1▲view on Lobsters ↗
    all of them →
  2. 2

    Lobsters community shares the post

    The article gains attention on Lobsters, where it reaches 14 points with early engagement.

  3. 1

    Baldino publishes enumeration of 4x4 sudoku solutions and structural variants

    A blog post counts all valid 4x4 sudoku grids and analyzes how many are structurally identical under digit relabeling. The post finds 288 total solutions but only 12 structurally distinct variants when symmetries are considered.

    “There are only twelve 4x4 sudokus! ... Or 288, depending on what counts as different solutions to you.”
    — baldino

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