Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
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?
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. . . .
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?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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 can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
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 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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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 triangles can you make on a circular pegboard that has nine pegs?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Exchange the positions of the two sets of counters in the least possible number of moves
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Here's a simple way to make a Tangram without any measuring or ruling lines.
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of this plaque design?
Can you cut up a square in the way shown and make the pieces into a triangle?
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?
Can you fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Make a cube out of straws and have a go at this practical challenge.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
Can you fit the tangram pieces into the outline of the child walking home from school?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outlines of these clocks?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?