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?
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?
What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
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?
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?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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?
A game for two players. You'll need some counters.
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. . . .
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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 greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
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?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outlines of these people?
Move just three of the circles so that the triangle faces in the opposite direction.
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
A variant on the game Alquerque
Can you cut up a square in the way shown and make the pieces into a triangle?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this telephone?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?