# Sudoku for Nikolaus 2005

## Explanation

Sudoku board: A board of 9x9 squares, subdivided into 3x3 boards of size 3x3:

Full Sudoku board: A Sudoku board with the squares filled with symbols 1, 2, ...,9, such that each row, each column and each 3x3 sub-board contains each symbol once, for example:

Sudoku puzzle: A Sudoku board with some squares filled with symbols 1, 2, ...,9, such that there is a unique full Sudoku board containing the given entries. Solving the puzzle means to fill the remaining squares. For example:

leads to the full Sudoku board shown above.

Nikolaus Sudoku puzzle: A Sudoku board with some squares filled with symbols 1, 2, ...,9. Solving the puzzle means to give the number of possibilities to put a symbol in one of the empty squares such that one gets a Sudoku puzzle (i.e., the remaining squares can be filled in a unique way to get a full Sudoku board). To prove that you have not just guessed the number, you also have to specify up to three of these possibilities. For example: