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?
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?
Here is a chance to play a version of the classic Countdown Game.
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?
Can you explain the strategy for winning this game with any target?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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. . . .
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.
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
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. . . .
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.
Can you discover whether this is a fair game?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
Can you beat the computer in the challenging strategy game?
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?
Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.
How good are you at estimating angles?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
To avoid losing think of another very well known game where the patterns of play are similar.
Here is a chance to play a fractions version of the classic Countdown Game.
An animation that helps you understand the game of Nim.
Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.
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.
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 hit?
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.
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?
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.
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Match pairs of cards so that they have equivalent ratios.
Can you find triangles on a 9-point circle? Can you work out their angles?
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
Match the cards of the same value.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.