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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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?
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
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.
An animation that helps you understand the game of Nim.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
Here is a chance to play a version of the classic Countdown Game.
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.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
To avoid losing think of another very well known game where the patterns of play are similar.
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.
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. . . .
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.
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...
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
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. . . .
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?
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
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 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.
A game in which players take it in turns to choose a number. Can you block your opponent?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you work out which spinners were used to generate the frequency charts?
Can you explain the strategy for winning this game with any target?
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?
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?
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
Match the cards of the same value.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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.
Here is a chance to play a fractions version of the classic Countdown Game.