## Help to generate the initial grid of sudoku

Everything about Sudoku that doesn't fit in one of the other sections

### Help to generate the initial grid of sudoku

Hi
I need your help to build a proper Sudoku puzzle by means of ILP modeling.

The model should derive an initial grid, from a sudoku solved, such that there exists a feasible Sudoku solution compatible to that grid and this solution is unique.

For example:

at the begining I have a sudoku solved like this:

then I remove two digits (to keep it simmetric)

remove other 2 digits

I continue to removing till the sudoku lose the constriction of unique solution

gianky_2007

Posts: 2
Joined: 18 December 2006

Wikipedia wrote:The three-letter abbreviation ILP can refer to the following concepts from computer science:

Instruction level parallelism
Integer linear programming
Inductive logic programming [1]
Information Leak Prevention

Besides, ILP can also refer to:

Independent Labour Party in the United Kingdom.
Integral Life Practice [2], a self-help system based on Integral theory (philosophy).
Individual Learning Plan, a teaching methodology.
International Language Programs, a Utah based program that sends people to teach English in Russia, Ukraine, and China.

Ok, I admit. I have no clue what ILP modeling is... But I know a bit about making sudoku puzzles.

If you want to create a puzzle by removing clues from a filled grid, your best option is to just remove clues and for each clue removed test if the grid is till unique. If you don't have a computer program to do this, there's plenty of free tools available on the web. The only other way I can think of is to first find all unavoidable sets in the grid and check before you remove a clue that all sets are still hit, but this method is way too slow even for an army of supercomputers.

There is no universal pattern (with less than 48 clues) that always gives unique puzzles, because all grids have very different properties.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

RW wrote:Ok, I admit. I have no clue what ILP modeling is...

ILP is:

Integer linear programming
gianky_2007

Posts: 2
Joined: 18 December 2006

gianky_2007 wrote:ILP is:

Integer linear programming

Given the options in wikipedia, I guessed that was the case. Maybe there is someone else here who understands your question better, but I think you should clarify it a bit. You have the full grid, then remove two symmetrical cluepairs as long as the solution stays unique. Yes, that's the way it is done. But, what is it that you want to achieve with ILP? You want to use it to select the clues to remove? As I said, there's only two ways to know if you can remove the clues, 1) remove them and test if the puzzle is still unique 2) find all unavoidable sets and check that each set that your clues are part of still has another given clue in them. Or are you looking for a third method?

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006