A game in which players take it in turns to choose a number. Can you block your opponent?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

If you have only four weights, where could you place them in order to balance this equaliser?

Can you complete this jigsaw of the multiplication square?

Use the interactivities to complete these Venn diagrams.

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Can you fit the tangram pieces into the outline of Little Ming?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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

An interactive activity for one to experiment with a tricky tessellation

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Train game for an adult and child. Who will be the first to make the train?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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.

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

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?

Exchange the positions of the two sets of counters in the least possible number of moves

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?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?