
Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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?

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?
Playing with numbers leads to a conjecture for the solution. Place value and summing a geometric series gives proof of the conjecture.
This article gives advice on getting started with exploring rich mathematical tasks.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
A game for 2 people. Take turns to move the counters 1, 2 or 3 spaces. The player to remove the last counter off the board wins.