# Sudoku for Nikolaus 2005

[Explanation] [New Nikolaus Game] [New Puzzle] [Recall Puzzle]

## 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:

The correct answer is **13**.

(The possibilities are:
8 in position (1, 3),
9 in (2, 2),
8 in (2, 5),
9 in (3, 3),
6 in (5, 1),
9 in (6, 2),
5 in (6, 3),
8 in (8, 2),
6 in (8, 7),
5 in (9, 2),
5 in (9, 3),
6 in (9, 3) or
8 in (9, 7).)

### References

Sudoku puzzles can be found in many newspapers and on the web, see Wikipedia for more information.

The programs for generating and solving Sudoku puzzles used on this page are written by me using GAP.

Questions and suggestions to Frank.Luebeck@Math.RWTH-Aachen.De.