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?
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?
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
What happens when you try and fit the triomino pieces into these two grids?
Use the clues to colour each square.
Can you cover the camel with these pieces?
What is the best way to shunt these carriages so that each train can continue its journey?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many different triangles can you make on a circular pegboard that has nine pegs?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many models can you find which obey these rules?
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....?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
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. . . .
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
These practical challenges are all about making a 'tray' and covering it with paper.
How many different rhythms can you make by putting two drums on the wheel?
Can you find all the different ways of lining up these Cuisenaire rods?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
How many trains can you make which are the same length as Matt's, using rods that are identical?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?