Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
If you have only four weights, where could you place them in order to balance this equaliser?
Choose a symbol to put into the number sentence.
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!
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
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 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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 complete this jigsaw of the multiplication square?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
These interactive dominoes can be dragged around the screen.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
An environment which simulates working with Cuisenaire rods.
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?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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....?
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?
A card pairing game involving knowledge of simple ratio.
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Use the sightings of the lion to guess the location of its lair.
A train building game for 2 players.
Can you find all the different ways of lining up these Cuisenaire rods?
How many different triangles can you make on a circular pegboard that has nine pegs?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
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?
Here is a chance to play a version of the classic Countdown Game.
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 can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.