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

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

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

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.

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

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 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?

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

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

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. . . .

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?

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...

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

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

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

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

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?

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

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

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

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

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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

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?

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 ?

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.

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

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?

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

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.

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?

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?

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.

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 square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

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

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?

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...