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