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12) Magic squares and cubes: Investigate magic tricks that use mathematics. 13) Loci and complex numbers 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?

15) Complex numbers and transformations 16) Euler’s identity: An equation that has been voted the most beautiful equation of all time, Euler’s identity links together 5 of the most important numbers in mathematics. This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. 18) Fermat’s last theorem: A problem that puzzled mathematicians for centuries – and one that has only recently been solved.

6) Continued fractions: These are fractions which continue to infinity.

The great Indian mathematician Ramanujan discovered some amazing examples of these.

19) Natural logarithms of complex numbers 20) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries.

The twin prime conjecture states that there are infinitely many consecutive primes ( eg. There has been a recent breakthrough in this problem.

2) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics.

Solve all the clues in a level to make it onto the leaderboard.5) Diophantine equations: These are polynomials which have integer solutions.Fermat’s Last Theorem is one of the most famous such equations.This is the British International School Phuket’s IB maths exploration (IA) page.This list is for SL and HL students – if you are doing a Maths Studies IA then go to this page instead.