Mind, Body, World- Foundations of Cognitive Science, 2013a

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Figure 8-3. An example Sudoku puzzle.
A Sudoku puzzle can be considered as a problem to be solved by relaxation labelling.
In relaxation labelling, sets of possible labels are available at different locations. For
instance, at the start of the puzzle given in Figure 8-3 the possible labels at every
blank cell are 1, 2, 3, 4, 5, 6, 7, 8, and 9. There is only one possible label (given in the
figure) that has already been assigned to each of the remaining cells. The task of
relaxation labelling is to iteratively eliminate extra labels at the ambiguous locations,
so that at the end of processing only one label remains.
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Figure 8-4. The “there can be only one” constraint propagating from the cell
labelled 5
In the context of relaxation labelling, Sudoku puzzles can be solved by propagating
different constraints through the grid; this causes potential labels to be
removed from ambiguous cells. One key constraint, called “there can be only one,”
emerges from the primary definition of a Sudoku puzzle. In the example problem
given in Figure 8-3, the digit 5 has been assigned at the start to a particular location,
which is also shown in Figure 8-4. According to the rules of Sudoku, this means that
this digit cannot appear anywhere else in the column, row, or cage that contains
372 Chapter 8