Minimum Sudoku

This page is concerned with the question of what is the smallest number of entries in a Sudoku puzzle that has a unique completion.

At the moment, there are examples of 17-hint uniquely completable Sudoku puzzles, but no known 16-hint examples. Hence I am collecting as many 17-hint examples as possible, in the hope that their analysis will yield some insight.

Currently I have a collection of distinct Sudoku configurations with 17 entries

Download the file containing all of them! (or the same file, but with the puzzles in minlex order).

This collection was mainly produced by my own software, although a few hundred have been sent to me by other people, in particular Glenn Fowler, Kohei Noshita and Håvard Graff. This collection is subject to Australian copyright law, but it may be freely used provided appropriate attribution is made to Gordon Royle and The University of Western Australia.

Creative Commons License
This work is licensed under a Creative Commons Attribution 2.5 License.

Now that new 17-clue Sudoku puzzles are becoming rarer to find, it would be sensible to try to retain puzzle-by-puzzle information about the initial discoverer.

Barring mistakes, these are guaranteed to be mathematically inequivalent in that no two of them can be translated to each other by any combination of the following operations

  1. Permutations of the 9 symbols,
  2. Transposing the matrix (that is, exchanging rows and columns),
  3. Permuting (ie. rearranging) rows within a single block,
  4. Permuting (ie. rearranging) columns within a single block,
  5. Permuting the blocks row-wise,
  6. Permuting the blocks column-wise.

This collection of operations forms a group of order 

9! x 6^8 x 2
Note: although not immediately apparent, rotations and reflections are already included in the above list because they can be expressed as combinations of these operations.

This list also contains all the ones that I have found on the Web to date. More precisely, it contains ones that are mathematically equivalent to the ones that I have found on the Web. They have been transmogrified into the particular form here simply for my personal computational reasons. I will give the sources for these in more detail shortly, but in summary they come from a Japanese blog, some postings on the forums at www.sudoku.com and my own computations.

If you have any more 17-hint examples, then please email them to me at 

gordon(AT)maths(DOT)uwa(DOT)edu(DOT)au
in plain text only. (All mail in HTML is automatically deleted due to my spam problems). I will automate this process (inlcuding detection of equivalence) shortly.

If you want to play with these (ie actually solve them), then I have a very simple-minded helper application in early development. Just click "transfer to helper" to activate it.

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