## A New Difficulty Metric for Soduku

- Status
- Finished
- Type
- Master Thesis
- Announcement date
- 30 May 2012
- Student
- Klemens Kranawetter
- Mentors
- Bernhard Geiger

- Research Areas

## Short Description

Sudoku games are usually classified according to - rather vague - difficulty levels such as “easy”, “challenging”, “devilish”, etc. But what is the underlying metric allowing such a classification? Clearly, while the number of clues give an indication of difficulty, there are certainly games with 21 clues which are more difficult to solve than a game with only 20. The literature therefore suggests to measure the difficulty of a game by the number of guesses a human player would have to take, or by the time he requires to solve a the game. Since the algorithms computing the difficulty depend on a variety of parameters, the estimated difficulty is almost as arbitrary as if a human would have obtained it.

We intend to define a single-letter number which does not depend on any parameters - and use information theory to get one: It is well known that 17 clues uniquely specify the solution of a Sudoku game. Therefore, the *entropy_of these 17 clues is equal to the entropy of the solution. Adding more clues does not increase the entropy. Adding more clues, however, increases the _redundancy*. We therefore assume that the difficulty of a game is somehow related to the redundancy of its clues: The higher the latter, the easier is the game. It is your task to evaluate this measure for a set of Sudoku games and verify if the assumption is true.

## Results

The project has been finished and the report can be downloaded here.