2.3. Spatial Representation#
See Denis Berthier’s Hidden Logic of Sudoku. https://github.com/denis-berthier.
A Sudoku solution is a unique selection and ordering of 81 ccells (value, row, column tuples) out of an exhaustive set of 729 ccells – where values, rows and columns can assume any value between 1 and 9, and Sudoku rules apply. Sudoku is a Finite Constraint Satisfaction problem, and the recognition of patterns and their resolutions in solving the puzzle are the constraint propagation techniques.
Sudoku puzzles are spatially represented as values on a 9 row by 9 column grid of cells. However, this is not the only possible spacial representation for Sudoku. The same puzzle can be represented as row numbers on a value x column number or any of the other 6 spatial domains:
values on a row x column grid (default)
row numbers on a value x column grid
column numbers on a value x row grid
values on a cell x box grid
box numbers on a value x cell grid
cell numbers on a value x box grid
The underlying puzzle logic is the same, it is only the perspective, that differs in each spatial representation.
However, each perspective, exposes patterns that are hidden in other perspectives. For example, a hidden single or hidden subset patten will be transformed into an exposed pattern in one of the five perspectives.
Viewing puzzles from different perspectiv0516es, come into its own with more complex patterns such as chains, loops, nets, bent hidden subsets, etc. Transforming to another domain may make it easier to spot exposed patterns that are hidden in the former domain.