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

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

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

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?

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. . . .

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.

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

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 maximise the area available to a grazing goat?

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.

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?

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?

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

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?

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

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

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...

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

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

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

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

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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.

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

Explore the effect of reflecting in two parallel mirror lines.

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

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

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. . . .

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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

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

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 ?

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

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?

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

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?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Use the differences to find the solution to this Sudoku.

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

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

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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?

Can you work out how to produce different shades of pink paint?

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?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .