Different combinations of the weights available allow you to make different totals. Which totals can you make?

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

How many winning lines can you make in a three-dimensional version of noughts and crosses?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

A jigsaw where pieces only go together if the fractions are equivalent.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

How many different symmetrical shapes can you make by shading triangles or squares?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

The clues for this Sudoku are the product of the numbers in adjacent squares.

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

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

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

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?

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

If you move the tiles around, can you make squares with different coloured edges?

Can you describe this route to infinity? Where will the arrows take you next?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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

Explore the effect of reflecting in two parallel mirror lines.

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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?

Is there an efficient way to work out how many factors a large number has?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?