Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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...
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 jigsaw where pieces only go together if the fractions are equivalent.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The clues for this Sudoku are the product of the numbers in adjacent squares.
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
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.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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?
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. . . .
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
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?
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?
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?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Use the differences to find the solution to this Sudoku.
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.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
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?
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.
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 rectangles where the value of the area is the same as the value of the perimeter?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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 hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
There are lots of different methods to find out what the shapes are worth - how many can you find?
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 ?
If you move the tiles around, can you make squares with different coloured edges?