The New Sudoku Players' Forum

[Mathimagics]

I'm investigating Sudoku Inequality puzzles. In particular whether there is any relationship between G, the minimum number of givens required for fixing a solution (in the standard 9x9 Sudoku puzzle), and R, the number of relationships required to fix a solution for Sudoku Inequality.

So it would be very useful to have a sample set of 100 or so sample grids with various G values.

The most useful format would be simply the givens, eg:

Code: Select all

000000010400000000020000000000050407008000300001090000300400200050100000000806000


Can anyone help?

[eleven]

Not sure what you want. There are minimal puzzles with 17 givens (almost 50000 known) up to 40 givens (2 known).
Do you want e.g. 5 for each number of givens ?

[Mathimagics]

Yes, that's just what I want!

[m_b_metcalf]

For givens counts between 20 and 29 you can mine the data stored in games_sample, referenced nearby.

Mike Metcalf

[Mathimagics]

Thanks, Mike!

I have also found eleven's advice on generating examples for G > 29 given over here.

Thanks to both of you, that should be enough to go on with

And thanks to dobrichev for the G = 38, 39, and 40 collections.

[blue]

Yes, that's just what I want!

Are you sure about that ?

For example:
The two 40 clue (minimal) puzzles, have the same solution grid.
That grid is also the (unique) solution to seven different 18 clue puzzles.

Code: Select all

(40 clues)
..........12.34567.345.6182..1.582.6..86....1.2...7.5...37.5.28.8..6.7..2.7.83615
..........12.34567.345.6182..1.582.6..86....1.2...785...37.5.2..8..6.7..2.7.83615

(18 clues)
.........81..........5.6..2......2.63...9..7.......85..6..1......5....3.....83...
....2..4.81.9......3..7...2...3.8..........7...91...5.......9.8..5.6.............
.7.....4.81..........5.6........8..63...9.....2..4........1.92...5..........8..1.
......34.81...4...9.................3...9...1.....7.5..6..1.9.8..5........7.8....
5...........9.4..7.3...6......35......8..2...6.9...8.........2.1......3...7...6..
5.6..............7....7..82....5.......69.4...2......3......92..8..........4.36..
.......4....93.....3.....82.4...8........2.716.9............9...8.......2.....6.5

(solution grid)
576821349812934567934576182741358296358692471629147853463715928185269734297483615

[eleven]

I also wondered, what kind of relationship Mathimagics is looking for (which could be researched with such sample puzzles)
I guess there are no good estimates for inequality sudokus, how many minimal puzzles there are with any fixed number of relations. I would have expected, that they would have to be calculated to see a relationship.