Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.
Which hexagons tessellate?
A huge wheel is rolling past your window. What do you see?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Four jewellers share their stock. Can you work out the relative values of their gems?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
Choose any three by three square of dates on a calendar page...
Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Replace each letter with a digit to make this addition correct.
ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
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?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Can you make sense of these three proofs of Pythagoras' Theorem?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
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 out.
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.
Can you use the diagram to prove the AM-GM inequality?
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
What are the missing numbers in the pyramids?
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played?