## general solution

Advanced methods and approaches for solving Sudoku puzzles

### general solution

I first heard about sudoku yesterday and after the first try I developped a pen and paper algorithm which solves any solvable sudoku without needing higher brain functions.

first step:
subdivide each field of a 9x9 sudoku grid into 9 squares (3x3). each of these subfields is used to represent a digit from 1 to 9, choose a numbering convention for the subfields, like

123
456
789

a cross in a subfield signifies that the corresponding digit cannot appear in this field.
example:

xx_
x__
_x_

(this field can be 3,5,6,7 or 9, but not 1,2,4 or 8)

second step: translate the sudoku into the new form.
For each supplied digit, fill the subfields not corresponding to the digit.
for example, 5 becomes

xxx
x_x
xxx

Definition: zone of influence: each field has a zone of influence, in the traditional sudoku these are the associated row, column and block (variants could define other zones of influence)

repeat

- choose a field with a single empty subfield.
- draw a zero in this empty subfield (zero is used to remember that the influence of this field has been computed, once and for all).
- in this field's zone of influence, add a cross in the same subfield of all other fields.

until the puzzle is solved.

(that works if you make no mistake, and the initial conditions determine a single solution)

the solved grid ooks like this

xx0 xxx x0x xxx
xxx x0x xxx xx0
xxx xxx xxx xxx etc...

last, translate the solution to numbers again

3 5 2 6 etc...

kind regards,
Dominik Schlaefli
Guest

What

Could you put that into layman's terms please?

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

Only works for the easy ones
Guest

Posts: 312
Joined: 25 November 2005

I could be wrong here but upon second look that could be what's referred to elsewhere on this site as carpet-bombing i.e. you put every available number in every box and then eliminate from there, which only works - generally speaking - with easy ones.

I just didn't understand your explanation, that's all. I wasn't making a sarcastic comment

Luna
lunababy_moonchild

Posts: 659
Joined: 23 March 2005

I came across sudoku for the first time yesterday and did much the same thing. Then I wrote a small computer program to do it for me. Trouble is, it only works for easy puzzles. It solved the May one on this website in about a zillionth of a second but it is stumped by harder ones. My challenge is to adapt the program to solve them too. Might still be at it in ten years ...
Guest

It can work if you then look for pairs of numbers within the boxes or along lines, then eliminate those numbers from the rest of the box or row
Guest

Pairs will help, but it's still not enough to solve all puzzles - not even those that don't require T&E.

More advanced techniques are required for the more difficult puzzles - lookup triplets, xwings, swordfish, nishio.
simes

Posts: 324
Joined: 11 March 2005
Location: UK