Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train can continue its journey?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
An activity making various patterns with 2 x 1 rectangular tiles.
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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....?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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 numbers 1 to 8 into the circles so that the four calculations are correct?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
How many models can you find which obey these rules?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
These practical challenges are all about making a 'tray' and covering it with paper.
In this matching game, you have to decide how long different events take.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Given the products of diagonally opposite cells - can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
In how many ways can you stack these rods, following the rules?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.