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
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Use the interactivities to complete these Venn diagrams.
If you have only four weights, where could you place them in order
to balance this equaliser?
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....?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
Can you complete this jigsaw of the multiplication square?
Here is a chance to play a version of the classic Countdown Game.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Work out how to light up the single light. What's the rule?
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.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
Using angular.js to bind inputs to outputs
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
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?
An environment which simulates working with Cuisenaire rods.
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
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. . . .
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.
An interactive activity for one to experiment with a tricky tessellation
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
A train building game for 2 players.
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 find all the different ways of lining up these Cuisenaire
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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 1 person to play on screen. Practise your number bonds
whilst improving your memory
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .