British Mathematical Olympiad
Congratulations to James Aaronson (Year 13, Upper Eighth), Sahl Khan (Year 12, Lower Eighth) and Zhaoxin Wang (Year 13, Upper Eighth) for their stunning performances in the first round of the British Mathematical Olympiad. James and Sahl both gained full marks, placing them 1st equal in the United Kingdom, and Zhaoxin was placed 19th equal.
The Olympiad is sat by the top 1,300 students in the United Kingdom, selected on the basis of how they performed in the Senior Maths Challenge. Round 1 consists of 6 very tough questions, to be attempted in 3½ hours.
Here are two of the problems solved by all three Paulines:
Consider a circle S. The point P lies outside S and a line is drawn through P, cutting S at distinct points X and Y. Circles S₁ and S₂ are drawn through P, which are tangent to S at X and Y, respectively. Prove that the difference of the radii of S₁ and S₂ is independent of the positions of P, X and Y.
Prove that the product of four consecutive positive integers cannot be equal to the product of two consecutive positive integers.
James, Sahl and Zhaoxin will now go on to Round 2, an even harder exam sat by the UK’s top 100 students.