50 lines
1.8 KiB
Markdown
50 lines
1.8 KiB
Markdown
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Su Doku (Japanese meaning number place) is the name given to a popular puzzle concept.
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Its origin is unclear, but credit must be attributed to Leonhard Euler
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who invented a similar, and much more difficult, puzzle idea called Latin Squares.
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The objective of Su Doku puzzles, however, is to replace the blanks (or zeros)
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in a 9 by 9 grid in such that each row, column, and 3 by 3 box contains
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each of the digits 1 to 9.
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Below is an example of a typical starting puzzle grid and its solution grid.
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~~~~~~~~~~~~~~~~~~~~~
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0 0 3 0 2 0 6 0 0
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9 0 0 3 0 5 0 0 1
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0 0 1 8 0 6 4 0 0
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0 0 8 1 0 2 9 0 0
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7 0 0 0 0 0 0 0 8
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0 0 6 7 0 8 2 0 0
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0 0 2 6 0 9 5 0 0
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8 0 0 2 0 3 0 0 9
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0 0 5 0 1 0 3 0 0
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~~~~~~~~~~~~~~~~~~~~~
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~~~~~~~~~~~~~~~~~~~~~
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4 8 3 9 2 1 6 5 7
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9 6 7 3 4 5 8 2 1
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2 5 1 8 7 6 4 9 3
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5 4 8 1 3 2 9 7 6
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7 2 9 5 6 4 1 3 8
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1 3 6 7 9 8 2 4 5
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3 7 2 6 8 9 5 1 4
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8 1 4 2 5 3 7 6 9
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6 9 5 4 1 7 3 8 2
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~~~~~~~~~~~~~~~~~~~~~
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A well constructed Su Doku puzzle has a unique solution and can be solved by logic,
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although it may be necessary to employ "guess and test" methods in order to eliminate
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options (there is much contested opinion over this).
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The complexity of the search determines the difficulty of the puzzle;
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the example above is considered easy because it can be solved by straight forward
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direct deduction.
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The 6K text file, [sudoku.txt](https://projecteuler.net/project/resources/p096_sudoku.txt) (right click and 'Save Link/Target As...'),
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contains fifty different Su Doku puzzles ranging in difficulty,
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but all with unique solutions (the first puzzle in the file is the example above).
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By solving all fifty puzzles find the sum of the 3-digit numbers found in the top
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left corner of each solution grid; for example, 483 is the 3-digit number found in the
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top left corner of the solution grid above.
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