Reasoning, convincing and proving

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Can you express every recurring decimal as a fraction?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Can you invert the logic to prove these statements?

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Can you find the hidden factors which multiply together to produce each quadratic expression?

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?