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 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?

A challenging activity focusing on finding all possible ways of stacking rods.

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

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

A Sudoku based on clues that give the differences between adjacent cells.

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.

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

How many different symmetrical shapes can you make by shading triangles or squares?

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?

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

A Sudoku that uses transformations as supporting clues.

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

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

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

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.

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?

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.

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?

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.

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

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

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

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.

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.

A Sudoku with clues given as sums of entries.

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?

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?

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?

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Given the products of adjacent cells, can you complete this Sudoku?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

You need to find the values of the stars before you can apply normal Sudoku rules.

A pair of Sudoku puzzles that together lead to a complete solution.

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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

This Sudoku, based on differences. Using the one clue number can you find the solution?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.