problem
Favourite
Circles ad infinitum
Age
16 to 18
Challenge level
A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
problem
Favourite
Direct logic
Age
16 to 18
Challenge level
Can you work through these direct proofs, using our interactive proof sorters?
problem
Mad robot
Age
16 to 18
Challenge level
Can you work out what happens when this mad robot sets off?
problem
Ap train
Age
16 to 18
Challenge level
An arithmetic progression is shifted and shortened, but its sum remains the same...
problem
Medicine half life
Age
14 to 18
Challenge level
A short challenge concerning the decay of medicines in the body.
problem
Speedy summations
Age
16 to 18
Challenge level
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
problem
Prime APs
Age
16 to 18
Challenge level
What can you deduce about prime numbers in arithmetic progression?