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?
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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....?
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 clues to colour each square.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
How many different rhythms can you make by putting two drums on the wheel?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
An activity making various patterns with 2 x 1 rectangular tiles.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below 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?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you find all the different ways of lining up these Cuisenaire rods?
Try this matching game which will help you recognise different ways of saying the same time interval.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Find out what a "fault-free" rectangle is and try to make some of your own.
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
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.
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?