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

Use the differences to find the solution to this Sudoku.

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?

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. . . .

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

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

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...

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

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

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

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?

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

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

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

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

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.

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

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

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

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

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

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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.

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?

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

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

There are lots of different methods to find out what the shapes are worth - how many can you find?

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 to. . . .

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Start with two numbers and generate a sequence where the next number is the mean of the last two 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?

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?

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?

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. . . .

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?

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.

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?

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

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

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.

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

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?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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