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## Project Euler 96: Solve SuDoku puzzles

#### Project Euler 96 Problem Description

Project Euler 96: Su Doku (Japanese meaning number place) is the name given to a popular puzzle concept. Its origin is unclear, but credit must be attributed to Leonhard Euler who invented a similar, and much more difficult, puzzle idea called Latin Squares. The objective of Su Doku puzzles, however, is to replace the blanks (or zeros) in a 9 by 9 grid in such that each row, column, and 3 by 3 box contains each of the digits 1 to 9. Below is an example of a typical starting puzzle grid and its solution grid.

 0 0 39 0 00 0 1 0 2 03 0 58 0 6 6 0 00 0 14 0 0 0 0 87 0 00 0 6 1 0 20 0 07 0 8 9 0 00 0 82 0 0 0 0 28 0 00 0 5 6 0 92 0 30 1 0 5 0 00 0 93 0 0
 4 8 39 6 72 5 1 9 2 13 4 58 7 6 6 5 78 2 14 9 3 5 4 87 2 91 3 6 1 3 25 6 47 9 8 9 7 61 3 82 4 5 3 7 28 1 46 9 5 6 8 92 5 34 1 7 5 1 47 6 93 8 2

A well constructed Su Doku puzzle has a unique solution and can be solved by logic, although it may be necessary to employ "guess and test" methods in order to eliminate options (there is much contested opinion over this). The complexity of the search determines the difficulty of the puzzle; the example above is considered easy because it can be solved by straight forward direct deduction.

The 6K text file, sudoku.txt (right click and ‘Save Link/Target As…’), contains fifty different Su Doku puzzles ranging in difficulty, but all with unique solutions (the first puzzle in the file is the example above).

By solving all fifty puzzles find the sum of the 3-digit numbers found in the top left corner of each solution grid; for example, 483 is the 3-digit number found in the top left corner of the solution grid above.

#### Analysis

Read an external file and parse into required format, solve Sudoku puzzles and add the first 3 digits: All in under 30 lines of Python.

Input file:
Each puzzle was converted from it’s native form into a string of 81 integers where zeros are blank squares. Any line with the word ‘Grid’ was ignored. The supplied data has been pre-validated, so sanity checks are not performed. Here’s an example for the puzzle listed in the problem description:
```Grid 01 003020600 900305001 001806400 008102900 700000008 006708200 002609500 800203009 005010300```
And here is what the solver expects:
`003020600900305001001806400008102900700000008006708200002609500800203009005010300`

Shortest Python Sudoku solver

#### Project Euler 96 Solution

Runs < 6 seconds in Pypy.

Use this link to get the Project Euler 96 Solution Pypy source.

#### Afterthoughts

• Grid #13 took the longest.
• Using PyPy instead of Python27 saved 85 seconds (18 times faster)
• 50 lines of 81 integer starting grids: pe96.prob
• 50 lines of 81 integer solutions: pe96.sol
• Project Euler 96 Solver here.
Project Euler 96 Solution last updated