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?
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.
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.
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. . . .
Can you discover whether this is a fair game?
To avoid losing think of another very well known game where the patterns of play are similar.
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. . . .
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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?
Here is a chance to play a fractions version of the classic Countdown Game.
Can you explain the strategy for winning this game with any target?
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. . . .
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you beat the computer in the challenging strategy game?
Here is a chance to play a version of the classic Countdown Game.
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?
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?
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.
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
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
How good are you at finding the formula for a number pattern ?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
An animation that helps you understand the game of Nim.
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
How good are you at estimating angles?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .
Use Excel to explore multiplication of fractions.
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
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.
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.
An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.
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?