There are lots of different methods to find out what the shapes are worth - how many can you find?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
This group tasks allows you to search for arithmetic progressions
in the prime numbers. How many of the challenges will you discover
Match the charts of these functions to the charts of their integrals.
Can you fit polynomials through these points?
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
Can you make a square from these triangles?
Which of these triangular jigsaws are impossible to finish?
These proofs are wrong. Can you see why?
Can you describe this route to infinity? Where will the arrows take you next?
Weekly Problem 13 - 2015
When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?
Weekly Problem 41 - 2007
The Queen of Spades always lies for the whole day or tells the truth for the whole day. Which of these statements can she never say?
Weekly Problem 20 - 2015
Four brothers give statements about the order they were born in. Can you work out which two are telling the truth?
Weekly Problem 35 - 2010
Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?
Weekly Problem 30 - 2015
How many ways are there of completing this table so that each row tells you how many there are of the numbers 1, 2, 3 and 4?
Weekly Problem 39 - 2016
In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?
Weekly Problem 44 - 2011
You have already used Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different, but can you still solve it...
Weekly Problem 51 - 2008
This grid can be filled up using only the numbers 1, 2, 3, 4, 5 so that each number appears just once in each row, once in each column and once in each diagonal. Which number goes in the centre square?
Weekly Problem 47 - 2014
Which digit replaces x in this crossnumber?
A collection of short Stage 3 and 4 problems on Reasoning, Justifying, Convincing and Proof.
Weekly Problem 11 - 2015
If it takes 852 digits to number all the pages of a book, what is the number of the last page?
Weekly Problem 7 - 2010
Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Weekly Problem 27 - 2011
Pizza, Indian or Chinese takeaway. Each teenager from a class only likes two of these, but can you work which two?
Weekly Problem 41 - 2016
The diagram shows a square, with lines drawn from its centre. What is the shaded area?
Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?