At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Can you make the numbers around each face of this solid add up to the same total?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

Given any positive integer n, Paul adds together the factors of n, apart from n itself. Which of the numbers 1, 3, 5, 7 and 9 can never be Paul's answer?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Which of the numbers shown is the product of exactly 3 distinct prime factors?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Here you have an expression containing logs and factorials! What can you do with it?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Find the highest power of 11 that will divide into 1000! exactly.

This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.

Weekly Problem 17 - 2010

The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Some extra resources to support work on Factors and Multiples at Secondary level.

A collection of resources to support work on Factors and Multiples at Secondary level.

A game in which players take it in turns to choose a number. Can you block your opponent?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross

This KS2 collection of activities encourages children to explore factors and multiples.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

A collection of short problems on factors, multiples and primes.

Working on these problems will help your students develop a better understanding of factors, multiples and primes.

Working on these problems will help you develop a better understanding of factors, multiples and primes.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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?

Can you design a die which rolls 'fairly' against mine?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Explore the patterns made by many beads sliding down a set of smooth rods

If three brothers will get £20 more if they do not share their money with their sister, how much money is there?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Weekly Problem 7 - 2013

Three of the angles in this diagram all have size $x$. What is the value of $x$?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Investigate Farey sequences of ratios of Fibonacci numbers.

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

There are lots of ideas to explore in these sequences of ordered fractions.

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are. . . .