data/problems/96.yml
---
:id: 96
:name: Su Doku
:url: https://projecteuler.net/problem=96
:content: "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.\n\n| \n\n| 0 0 3 \n9 0 0 \n0 0 1 | 0 2 0 \n3 0 5 \n8 0 6
| 6 0 0 \n0 0 1 \n4 0 0 |\n| 0 0 8 \n7 0 0 \n0 0 6 | 1 0 2 \n0 0 0 \n7 0 8
| 9 0 0 \n0 0 8 \n2 0 0 |\n| 0 0 2 \n8 0 0 \n0 0 5 | 6 0 9 \n2 0 3 \n0 1 0
| 5 0 0 \n0 0 9 \n3 0 0 |\n\n |  \n | \n\n| 4
8 3 \n9 6 7 \n2 5 1 | 9 2 1 \n3 4 5 \n8 7 6 | 6 5 7 \n8 2 1 \n4 9 3 |\n| 5
4 8 \n7 2 9 \n1 3 6 | 1 3 2 \n5 6 4 \n7 9 8 | 9 7 6 \n1 3 8 \n2 4 5 |\n| 3
7 2 \n8 1 4 \n6 9 5 | 6 8 9 \n2 5 3 \n4 1 7 | 5 1 4 \n7 6 9 \n3 8 2 |\n\n
|\n\nA 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.\n\nThe 6K
text file, [sudoku.txt](project/resources/p096_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).\n\nBy
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.\n\n"