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.

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.

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?

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

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

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

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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?

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?

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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 different shapes that can be made by joining five equilateral triangles edge to edge.

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

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

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

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

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

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.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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

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.

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?

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

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?