British Mathematical Olympiad
The British Mathematical Olympiad is a national math competition held in the United Kingdom. Solvers who score over a certain threshold in the Senior Mathematical Challenge are automatically entered to the first round, but others can register for the first round.
Structure
The British Mathematical Olympiad is divided into two rounds. In the first round (BMO 1), solvers have 3.5 hours to solve 6 problems. High scorers can move on into the second round (BMO 2), where solvers have 3.5 hours to solve 4 problems.
For both rounds, each problem is worth 10 points. Like most Olympiads, complete solutions are required in order to get full credit.
Participants who submit a solution with the highest quality in BMO 2 can earn the Christopher Bradley elegance prize.
Resources
21-th Mathematical Olympiad 1985 Problem 5
A circular hoop of radius 4 cm is held fixed in a horizontal plane. A cylinder with radius 4 cm and length 6 cm rests on the hoop with its axis horizontal, and with each of its two circular ends touching the hoop at two points. The cylinder is free to move subject to the condition that each of its circular ends always touches the hoop at two points. Find, with proof, the locus of the centre of one of the cylinder’s circular ends.
vladimir.shelomovskii@gmail.com, vvsss
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