![]() ![]() Previously the researchers have been able to use their principles to analyse a railway accident in the Clayton Tunnel near Brighton when the telegraph was introduced in 1861. The interaction between the shifting colour squares and the logical deductions of the Sudoku puzzle solver is a good illustration of the unusual quality of this "Empirical Modelling" approach. It is of particular relevance for artificial intelligence, computer graphics, and educational technology. The interplay between logic and perception, as it relates to interactions between computers and humans is viewed as key to the building of better software. The method can be applied to other creative problems and he is exploring how this experimental modelling technique can be used in educational technology and learning. For doctoral researcher Antony Harfield it is a way of exploring how logic and perception interact using a radical approach to computing called Empirical Modelling. ![]() However the colour Sudoku is more than just a game to the University of Warwick Computer Scientists. Sudoku players can test this for themselves at: (NB page requires Flash 9) ![]() Players also can gain additional clues by changing the colour assigned to the each digit and watching the unfolding changes in the pattern of colours. If a black square is encountered then a mistake has been made. More usefully an empty square that has the same colour as a completed square must contain the same digit. This gives players major clues as darker coloured empty squares imply fewer number possibilities. The empty square's colour is the combination of the colours assigned to each possible digit. Empty squares are coloured according to which digits are possible for that square taking account of all current entries in the square's row, column and region. Squares containing a digit are coloured according to the digit's colour. Because some blue cells are invalid, we can declare all blue cells unsuitable for digit 1.The colour Sudoku adds another dimension to solving the puzzle by assigning a colour to each digit. There are 2 blue cells in row 1, box 2 and column 5. ![]() It is easy to see that it would be impossible for all blue cells to contain digit 1. Now either all blue cells must contain digit 1 or all green cells. Here is an example that shows how colors can cause a contradiction.Īll the candidates for digit 1 are highlighted. It cannot sustain a candidate for digit 3. There is no middle ground in which some blue cells and some green cells contain digit 3.Ĭell r2c6 can see both colors. Now either all blue cells must contain digit 3 or all green cells. Notice that row 9, column 9 and box 9 all have 2 candidates for digit 3, which now have opposite colors. In the example, green and blue colors have been applied. We can use colors to help us remember which candidates must be true or false simultaneously. In coloring terminology, these candidates form a conjugate pair. When a row, column or box contains only 2 candidates for a digit, one of them must be true and the other must be false. The following example demonstrates the principle:Īll the candidates for digit 3 are highlighted. Simple Colors Simple Colors is a subtype of coloring which only uses 2 colors. ![]()
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