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?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the differences to find the solution to this Sudoku.
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 describe this route to infinity? Where will the arrows take you next?
It is known that the area of the largest equilateral triangular
section of a cube is 140sq cm. What is the side length of the cube?
The distances between the centres of two adjacent faces of. . . .
A hexagon, with sides alternately a and b units in length, is
inscribed in a circle. How big is the radius of the circle?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
A plastic funnel is used to pour liquids through narrow apertures.
What shape funnel would use the least amount of plastic to
manufacture for any specific volume ?
An aluminium can contains 330 ml of cola. If the can's diameter is
6 cm what is the can's height?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Why does this fold create an angle of sixty degrees?
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
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 ?
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. . . .
Explore when it is possible to construct a circle which just
touches all four sides of a quadrilateral.
There are many different methods to solve this geometrical problem - how many can you find?
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
There are lots of different methods to find out what the shapes are worth - how many can you find?
A square of area 40 square cms is inscribed in a semicircle. Find
the area of the square that could be inscribed in a circle of the
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Many numbers can be expressed as the difference of two perfect
squares. What do you notice about the numbers you CANNOT make?
Your school has been left a million pounds in the will of an ex-
pupil. What model of investment and spending would you use in order
to ensure the best return on the money?
If a sum invested gains 10% each year how long before it has
doubled its value?
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?
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?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.
Which set of numbers that add to 10 have the largest product?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Find the sum of the series.
Which of these games would you play to give yourself the best possible chance of winning a prize?
Find the decimal equivalents of the fractions one ninth, one ninety
ninth, one nine hundred and ninety ninth etc. Explain the pattern
you get and generalise.
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
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?
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?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
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
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you find the area of a parallelogram defined by two vectors?
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
What is the same and what is different about these circle
questions? What connections can you make?