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?

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.

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

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

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

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

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.

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?

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?

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?

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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

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

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

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.

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

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?

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?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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.

Four small numbers give the clue to the contents of the four surrounding cells.

A Sudoku that uses transformations as supporting clues.

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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?

Find out about Magic Squares in this article written for students. Why are they magic?!

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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

A few extra challenges set by some young NRICH members.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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?

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?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

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?