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?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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?

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?

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 tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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?

A Sudoku with clues given as sums of entries.

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.

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

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

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.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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

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?

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?

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...

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Can you find all the different triangles on these peg boards, and find their angles?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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 package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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

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

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

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?

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

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?

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?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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.