Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
Find out what a "fault-free" rectangle is and try to make some of
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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?
An odd version of tic tac toe
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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....?
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 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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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.
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?
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.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Exchange the positions of the two sets of counters in the least possible number of moves
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
A variant on the game Alquerque
How many different rhythms can you make by putting two drums on the
Try out the lottery that is played in a far-away land. What is the
chance of winning?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Move just three of the circles so that the triangle faces in the
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?
Using angular.js to bind inputs to outputs
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Can you fit the tangram pieces into the outline of the child walking home from school?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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 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
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?
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 fit the tangram pieces into the outline of Little Fung at the table?