Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Find out what a "fault-free" rectangle is and try to make some of
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
An odd version of tic tac toe
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
Here is a chance to play a version of the classic Countdown Game.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a 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....?
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?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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 fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
A variant on the game Alquerque
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?
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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!
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Move just three of the circles so that the triangle faces in the
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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.
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.
How many different rhythms can you make by putting two drums on the
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Exchange the positions of the two sets of counters in the least possible number of moves
An interactive activity for one to experiment with a tricky tessellation
Can you fit the tangram pieces into the outlines of the chairs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Work out how to light up the single light. What's the rule?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?