To mark the Turing centenary (who isn’t?) a new competition has been launched:

To celebrate this centenary, we have developed a collection of one-person games played on a Turing tape.

An example is given on the competition website. According to a set of movement rules, the player must:

Construct a sequence of moves that when begun in a state with one coin on one of the squares of a Turing tape (and all other squares empty) ends with one coin at a displacement of 12 squares from the initial position (and all other squares empty).

The full example and worked solution is available via the competition website. This says of the games:

So far as we are aware, the games are entirely novel and haven’t been studied before (except for a couple of isolated examples). The games quickly become too difficult to solve by hand and so demand machine support for their solution. They are based on the mathematical theory of cyclotomic polynomials. Although the games can be solved with little or no knowledge of the underlying mathematics, we think that this combination of mathematics and computer programming is very relevant to celebrating Turing’s legacy.

The games are subject of a competition in which participants must solve a series of problems culminating in a grand final in August.

Eligibility:

Anyone may take part in all rounds (including the final). To win a prize you must, however, be registered as a student at a UK educational institution in one of the following categories: school (i.e. pre higher education), undergraduate at a university or college, postgraduate at a university or college.

Prizes:

Prizes in each of the three categories pre-university, undergraduate and postgraduate student will be awarded as follows.
1st Prize.
£150
Signed copy of Algorithmic Problem Solving by Roland Backhouse.
MATLAB and Simulink Student Version
2nd Prize.
£50
Signed copy of Algorithmic Problem Solving by Roland Backhouse.
MATLAB and Simulink Student Version
3rd Prize.
Signed copy of Algorithmic Problem Solving by Roland Backhouse.
MATLAB and Simulink Student Version
Everyone who registers for the competition is entitled to a 20% discount on the price of a copy of the book Algorithmic Problem Solving by Roland Backhouse when purchased from the publisher, John Wiley and Sons. Details of how to claim the discount are sent with the email confirming registration.

All details, how to register and a FAQ is available via the website: Turing-Tape Games: A Challenge in Algorithmic Problem Solving.