Your Post-16 Solutions

Tetra Inequalities

Age 16 to 18
Challenge Level

Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?

Pythagoras for a Tetrahedron

Age 16 to 18
Challenge Level

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.

Tetra Perp

Age 16 to 18
Challenge Level

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.

A Very Shiny Nose?

Age 16 to 18
Challenge Level

This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

Tetra Slice

Age 16 to 18
Challenge Level

Can you prove that a quadrilateral drawn inside a tetrahedron is a parallelogram?

Amicable Arrangements

Age 16 to 18
Challenge Level

Three of Santa's elves and their best friends are sitting down to a festive feast. Can you find the probability that each elf sits next to their bestie?

The Koch Snowflake

Age 16 to 18
Challenge Level

Explore the strange geometrical properties of the Koch Snowflake.