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?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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

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

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

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.

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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?

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.

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.

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

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?

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

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?

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

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.

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?

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?

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?

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?

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

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.

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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?

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

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

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.

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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.

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

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

A few extra challenges set by some young NRICH members.

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

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

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.

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?

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