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.

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

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

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.

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?

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.

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

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?

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?

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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

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

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

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

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?

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?

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

Use the differences to find the solution to this Sudoku.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

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.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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.

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?

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

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Solve the equations to identify the clue numbers in this Sudoku problem.

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

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

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Use the clues about the shaded areas to help solve this sudoku

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

Charlie and Abi 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?

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

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

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?

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

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