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?

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?

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.

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

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

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

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

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

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

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.

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

This challenge extends the Plants investigation so now four or more children are involved.

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 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.

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

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

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.

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?"

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

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?

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 few extra challenges set by some young NRICH members.

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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

Find out what a "fault-free" rectangle is and try to make 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?

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.

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?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?

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

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

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

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?