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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. . . .
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.
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.
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
If a sum invested gains 10% each year how long before it has doubled its value?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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?
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 ?
According to an old Indian myth, Sissa ben Dahir was a courtier for a king. The king decided to reward Sissa for his dedication and Sissa asked for one grain of rice to be put on the first square. . . .
Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.
There are lots of different methods to find out what the shapes are worth - how many can you find?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
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?
What is the smallest number with exactly 14 divisors?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Use the differences to find the solution to this Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Can you maximise the area available to a grazing goat?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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. . . .
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Can you describe this route to infinity? Where will the arrows take you next?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
How many different symmetrical shapes can you make by shading triangles or squares?
Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
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. . . .
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
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. . . .
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.
What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.
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?
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?
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?
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?