If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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. . . .
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Which set of numbers that add to 10 have the largest product?
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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.
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
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?
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?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
If you move the tiles around, can you make squares with different coloured edges?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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. . . .
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Here's a chance to work with large numbers...
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
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 there an efficient way to work out how many factors a large number has?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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.
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?
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?
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 clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Explore the effect of reflecting in two parallel mirror lines.
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?
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?
Can you describe this route to infinity? Where will the arrows take you next?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?