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?
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.
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...
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. . . .
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
A jigsaw where pieces only go together if the fractions are equivalent.
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?
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.
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 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?
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 ?
How many different symmetrical shapes can you make by shading triangles or squares?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
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. . . .
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 you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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?
Use the differences to find the solution to this Sudoku.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Is there an efficient way to work out how many factors a large number has?
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?
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 guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
If you move the tiles around, can you make squares with different coloured edges?
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 ?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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?
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
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 work out the dimensions of the three cubes?
Here's a chance to work with large numbers...
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...