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?
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?
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 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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Can you find all the different ways of lining up these Cuisenaire rods?
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. . . .
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
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.
How many different triangles can you make on a circular pegboard that has nine pegs?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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?
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....?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
These practical challenges are all about making a 'tray' and covering it with paper.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Can you find all the different triangles on these peg boards, and find their angles?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
Find out what a "fault-free" rectangle is and try to make some of your own.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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.
In this matching game, you have to decide how long different events take.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.