Can all unit fractions be written as the sum of two unit fractions?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

Play around with sets of five numbers and see what you can discover about different types of average...

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

Can you do a little mathematical detective work to figure out which number has been wiped out?

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.

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Which armies can be arranged in hollow square fighting formations?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?