This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Find out what a "fault-free" rectangle is and try to make some of
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
What happens when you round these numbers to the nearest whole number?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
An investigation that gives you the opportunity to make and justify
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you arrange 5 different digits (from 0 - 9) in the cross in the
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Find out about Magic Squares in this article written for students. Why are they magic?!
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?