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?
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?
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?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
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?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
An activity making various patterns with 2 x 1 rectangular tiles.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
How many models can you find which obey these rules?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
These practical challenges are all about making a 'tray' and covering it with paper.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
What is the best way to shunt these carriages so that each train can continue its journey?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Find out what a "fault-free" rectangle is and try to make some of your own.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
The Zargoes use almost the same alphabet as English. What does this birthday message say?