Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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....?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
Can you find all the different triangles on these peg boards, and find their angles?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Find out what a "fault-free" rectangle is and try to make some of your own.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Can you explain the strategy for winning this game with any target?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Work out the fractions to match the cards with the same amount of money.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
A generic circular pegboard resource.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you fit the tangram pieces into the outline of this telephone?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.