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.
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?
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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?
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. . . .
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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?
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. . . .
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Use the differences to find the solution to this Sudoku.
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...
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.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Can you work out the dimensions of the three cubes?
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
Can you maximise the area available to a grazing goat?
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 to. . . .
Why does this fold create an angle of sixty degrees?
Explore the effect of reflecting in two parallel mirror lines.
Can you describe this route to infinity? Where will the arrows take you next?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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?
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?
Explore the effect of combining enlargements.
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?
What is the smallest number with exactly 14 divisors?
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
Can all unit fractions be written as the sum of two unit fractions?
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?