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 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.

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

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

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 task encourages you to investigate the number of edging pieces and panes in different sized windows.

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 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 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?

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

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

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.

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

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?

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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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?

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

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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

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?

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?

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.

A few extra challenges set by some young NRICH members.

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

In this matching game, you have to decide how long different events take.

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

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

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

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.

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 out what a "fault-free" rectangle is and try to make some of your own.

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?

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

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?

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

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?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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.

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.

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.

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.

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

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?