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?

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?

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.

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

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?

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?

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

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.

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

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.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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?

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

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

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?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

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?

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.

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

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

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

A few extra challenges set by some young NRICH members.

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

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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

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?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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.

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

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?

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".

How many different symmetrical shapes can you make by shading triangles or squares?

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

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?

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

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?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

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

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

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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.