Welcome back to Problem of the Week.
You may notice that there are two problems this week – Problem 36 is released a week early to provide a bit more time to solve. Going forward, the 1-week-1-problem structure will be mainly followed.
The solution to Problem 35 will be released on 7th October, and the solution to Problem 36 will be released on 14th October.
In the spirit of the Senior Maths Challenge, here is a geometry problem:
An inscribed equilateral triangle is constructed within a circle. Along each side of the triangle lies the largest square that can fit within the circle.
a) What fraction of the circle is blue in this diagram?
bi) Consider the diagram in 3D – An inscribed tetrahedron within a sphere, and along each face of the tetrahedron lies the largest cube within the sphere. What fraction of the sphere are made up of the cubes?
bii) Deduce that the 4 cubes will not overlap.