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?

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?

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?

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.

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.

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?

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?

Can you find all the different ways of lining up these Cuisenaire rods?

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?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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?

A Sudoku with clues given as sums of entries.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Find out what a "fault-free" rectangle is and try to make some of your own.

Two sudokus in one. Challenge yourself to make the necessary connections.

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.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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.

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?

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?

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....?

How many different triangles can you make on a circular pegboard that has nine pegs?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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?

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.

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?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Given the products of diagonally opposite cells - can you complete this Sudoku?

How many models can you find which obey these rules?

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.

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.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

Two sudokus in one. Challenge yourself to make the necessary connections.