First prize was shared by two teams: Ross Lowe, for "Pybook", and Nathanael Alcock and Kit Richardson, for "Non-Linear Reflections".

13-year-old Ross Lowe's "Pybook" is a wonderfully ambitious project which brings together maths and social media. In Ross's own words, taken from his detailed user manual: "This is Pybook: the 'py' stands for Python and the 'book' is from Facebook. Have you been paying attention?". Once you have registered online, you may unlock a range of maths-based quizzes and games. Your scores are automatically posted onto your online "homepage", for the admiration of friends and family. Pybook lets you send messages and questions to other users, for example, when you are stuck with a homework problem.

The judges were impressed by the sheer scope and ambition of Ross's vision. Ross himself gives some credit to his Mum, for telling him when to stop adding new features! By the way, look out for Ross's forthcoming project on Kickstarter ...

Nathanael and Kit have investigated an intriguing and novel idea. At the fairground, in a "hall of mirrors" we find our reflection is distorted by curved mirrors. But what if a reflection could be generated by any curve (even one with loops and crossing points)? Nathanael and Kit have derived a mathematical equation which tells one how a figure F(t) may be reflected by a mirror M(t) to produce a reflection R(t), where F, M and R are parametrically-defined curves. To compute and visualise the reflections, they have written a Python program which uses the SymPy library for symbolic algebra. The results are rather beautiful:

Second prize was awarded to 16-year-old Alexander Taylor, for a CPU emulator called Algomac. Alexander has clearly learned a great deal from a recent work placement at Douglas Instruments, and his teachers. His emulator, written entirely in Python, is powerful and efficient. To help us understand how it works, Alexander included several different "programs" (sets of instructions) which the emulator can interpret. This project demonstrates a deep understanding of the foundations of computing. Had the Challenge been run by our colleagues in Computer Science, I'm sure Alexander's work would have won first prize!

Third prize was awarded to 16-year-old Gregory Brooks, for the "Prime Number Calculator & RSA Encryption Demonstration". Gregory's program makes use of the fact that prime numbers can be expressed as 6x + 1 or 6x - 1, in order to optimize the search for primes. Gregory presents an implementation of the RSA algorithm for encryption and decryption of  messages. The RSA algorithm relies on the fact that it is far easier for computers to multiply two large primes together, than to split an even larger number into a pair of prime constituents. Gregory demonstrates a good understanding of this algorithm, which has become the basis for internet security around the world.

Just missing out on prizes were projects by Vaibhav Krishnakumar (Ibstock Place School) and Robin Hartland (Sutton Grammar School). Vaibhav's entry, "Mental Maths Games", was inspired by his experience of the different ways in which maths is taught in schools in India and the UK. His games are designed to improve the speed at which UK students can undertake mental arithmetic. Robin's entry, "Enigmaths", was inspired by a family visit to Bletchley Park. The program computes the amount of time it would take to break a code from the Enigma machine. It is notable for its vivid descriptions of the futility of the task: