sudoku

Sudoku is a popular logical game. The name comes from Japanese "Suji Wa Dokushin Ni Kagiru," but its origin is not japaneese. The game was published in eighties of 20^th century under the name "Number Place" in an american puzzle magazine, and it bacame popular in Japan. But the real boom came in 2005, when sudoku spread the whole world and has become massively popular. Today sudoku is one of the most famous and most frequent games distributed by magazines, newspaper and internet.

A table with nine rows and nine columns contains several fields with a given number.

Your goal is to

fill the sudoku table with numbers from 1 to 9 so that any number in any row, column, or highlighted 3x3 section does not repeat.

Worded differently, it means that each row, column and each of the nine 3x3 sections must contain numbers 1-9 (1, 2, 3, 4, 5, 6, 7, 8, 9).

In order to have a single solution, the sudoku must have at least 17 given numbers. We don't know any sudoku with 16 numbers and a single solution.

On the other hand, it does not directly imply that sudoku with 17 given numbers must be more difficult than the one with more given numbers. Here is an example with two sudokus with 64 unknown fields: first sudoku is one of the easiest, while the second cannot be solved without using the method of trial and error.

You can use paper, pencil, mouse, keyboard and your brain. In the end, you find yourself left alone with your logic reasoning. You are not allowed to consult the solution with any other person.