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?

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

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.

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?

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

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

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

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?

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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

Use the differences to find the solution to this Sudoku.

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

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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.

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.

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 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?

In a three-dimensional version of noughts and crosses, how many winning lines can you 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.

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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

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

Think of two whole numbers under 10. Take one of them and add 1. Multiply by 5. Add 1 again. Double your answer. Subract 1. Add your second number. Add 2. Double again. Subtract 8. Halve this. . . .

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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

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?

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. . . .

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

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. . . .

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try. . . .

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

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?

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?

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

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?

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

Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.

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

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

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

Which set of numbers that add to 10 have the largest product?

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?

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.

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

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.