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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Here is a chance to play a version of the classic Countdown Game.
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 explain the strategy for winning this game with any target?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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?
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!
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
A generic circular pegboard resource.
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?
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?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Use the interactivities to complete these Venn diagrams.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
If you have only four weights, where could you place them in order to balance this equaliser?
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
Can you fit the tangram pieces into the outline of this telephone?
Can you logically construct these silhouettes using the tangram pieces?
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Hover your mouse over the counters to see which ones will be removed. Click to remove 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?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .