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Function Description

Returns the solution to a Sudoku-style puzzle if given input in a suitable form. See also Standard Sudoku Solver and Killer Sudoku Solver, which provide interactive ways of accessing this tool.


The easiest way to understand the required input format is to consider the nature of a Killer Sudoku puzzle. In this Sudoku-variant, there are various groupings of cells scattered across the 9 by 9 grid (usually contiguous). These each have defined numbers of cells within them and a defined total (e.g. there might be a grouping of 2 cells the total of which needs to be 3 (and thus the first cell of the pair forming this group can only be 1 and the second 2 or vice-versa). Each entry in a group needs to be different, so there are at most 9 cells in any one group. For, say, the ’th group, we thus know at outset the number of cells, , in the group, the sum of the entries, , of the cells in the group and the coordinates of each cell,


The required input form involves an array of bytes, in groups of 20 consecutive entries (so if there are 30 groups then the input array needs to be  entries long), ordered as follows:


-          First entry = number of cells in the group, i.e.

-          Second entry = required sum of entries in these cells, i.e.

-          Third entry = -coordinate of the first cell in the group, i.e.

-          Fourth entry = -coordinate of the first cell in the group, i.e.

-          Fifth entry = -coordinate of the second cell in the group, i.e.

-          Sixth entry = -coordinate of the second cell in the group, i.e. , etc. (with the last entries in the group of 20 ignored if the group has less than 9 cells in it).


Also takes as a further input the type of the Sudoku puzzle (i.e. ‘Killer’, ‘Standard’, ‘Samurai’ or ‘General’). These simplify the inputs (for the first three) so that you do not need each time to specify the standard features of the puzzle. For example, with a Killer Sudoku puzzle, we can think of the overarching grid layout as defining a further set of groups, since each row, column and principal 3-by-3 group needs to contain all the numbers 1 to 9. They can therefore be coded as akin to a group like the one above but with ,  and the remaining entries in the set of 20 consecutive bytes defining the positioning of each cell (from 1 to 9). If you choose the ‘General’ type you will need to enter these groups yourself. The solver will also not then check the input data for consistency (e.g. with a Killer Sudoku puzzle all cell coordinates in the 9 by 9 grid need to be in the range 1 to 9, each cell needs to appears just once in the definition of groups as above, and the sum of all of the group totals is 405).


With a ‘Standard’ Sudoku puzzle, the same input format is used as above. Each known entry in the grid forms corresponds to its own group, with ,  = the (known) entry in the cell, and  identifying the location of that cell.


‘Samurai’ Sudoku involves a more complex grid, but can be solved in a similar fashion, just with more initial groups.


The solver uses an exhaustive search approach, so should identify a unique solution if there is one. However, it does include an iteration upper limit which you might need to set reasonably high for more complicated puzzles.


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Links to:

-          Interactively run function

-          Interactive instructions

-          Example calculation

-          Output type / Parameter details

-          Illustrative spreadsheet

-          Other Mathematical puzzle functions

-          Computation units used

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