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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
An environment which simulates working with Cuisenaire rods.
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
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....?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
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!
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?
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 find all the different ways of lining up these Cuisenaire
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 complete this jigsaw of the multiplication square?
Find out what a "fault-free" rectangle is and try to make some of
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Here is a chance to play a version of the classic Countdown Game.
Can you find all the different triangles on these peg boards, and
find their angles?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Choose a symbol to put into the number sentence.
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Train game for an adult and child. Who will be the first to make the train?
A card pairing game involving knowledge of simple ratio.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
A generic circular pegboard resource.
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?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
A train building game for 2 players.
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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
An interactive activity for one to experiment with a tricky tessellation
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.