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?
Which of these games would you play to give yourself the best possible chance of winning a prize?
An aluminium can contains 330 ml of cola. If the can's diameter is
6 cm what is the can's height?
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 ?
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 ?
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 is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Chris and Jo put two red and four blue ribbons in a box. They each
pick a ribbon from the box without looking. Jo wins if the two
ribbons are the same colour. Is the game fair?
Why does this fold create an angle of sixty degrees?
How many pairs of numbers can you find that add up to a multiple of
11? Do you notice anything interesting about your results?
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
A napkin is folded so that a corner coincides with the midpoint of
an opposite edge . Investigate the three triangles formed .
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at
100°C (212°Fahrenheit). Is there a temperature at which
Celsius and Fahrenheit readings are the same?
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
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
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
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
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
Two ladders are propped up against facing walls. The end of the
first ladder is 10 metres above the foot of the first wall. The end
of the second ladder is 5 metres above the foot of the second. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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...
Use the differences to find the solution to this Sudoku.
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
What is the smallest number with exactly 14 divisors?
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 number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
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. . . .
Investigate how you can work out what day of the week your birthday
will be on next year, and the year after...
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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.
If the hypotenuse (base) length is 100cm and if an extra line
splits the base into 36cm and 64cm parts, what were the side
lengths for the original right-angled triangle?
A circle is inscribed in a triangle which has side lengths of 8, 15
and 17 cm. What is the radius of the circle?
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 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?
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?
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
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. . . .
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
The area of a square inscribed in a circle with a unit radius is,
satisfyingly, 2. What is the area of a regular hexagon inscribed in
a circle with a unit radius?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Each of the following shapes is made from arcs of a circle of
radius r. What is the perimeter of a shape with 3, 4, 5 and n
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?