Use the differences to find the solution to this Sudoku.

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

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

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

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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

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.

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?

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

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

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?

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

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

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

If a sum invested gains 10% each year how long before it has doubled its value?

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

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?

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

Can you find the area of a parallelogram defined by two vectors?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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. . . .

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

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 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

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 ?

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

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

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

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

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. . . .

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.

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

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

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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?

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?

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?

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?

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

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

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?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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

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?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Explore the effect of combining enlargements.

Explore the effect of reflecting in two parallel mirror lines.

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