Find out about Magic Squares in this article written for students. Why are they magic?!
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you replace the letters with numbers? Is there only one
solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
An investigation that gives you the opportunity to make and justify
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Number problems at primary level that require careful consideration.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of