Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Find out about Magic Squares in this article written for students. Why are they magic?!
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
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?
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.
Charlie and Lynne put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
How many different symmetrical shapes can you make by shading triangles or squares?
An investigation that gives you the opportunity to make and justify predictions.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
An activity making various patterns with 2 x 1 rectangular tiles.
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?