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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?

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Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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An activity centred around observations of dots and how we visualise number arrangement patterns.

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Have a look at these photos of different fruit. How many do you see? How did you count?

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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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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?

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Design an arrangement of display boards in the school hall which fits the requirements of different people.

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How will you go about finding all the jigsaw pieces that have one peg and one hole?

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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?

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Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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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?

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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?

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What is the best way to shunt these carriages so that each train can continue its journey?

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The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

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These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Can you make a 3x3 cube with these shapes made from small cubes?

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Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

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Can you fit the tangram pieces into the outline of Mah Ling?

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Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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How many different triangles can you make on a circular pegboard that has nine pegs?

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Can you fit the tangram pieces into the outlines of the people?

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Can you find a way of counting the spheres in these arrangements?

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How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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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?

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Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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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.

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A shape and space game for 2, 3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board.

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Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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How many moves does it take to swap over some red and blue frogs? Do you have a method?

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If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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Which of these dice are right-handed and which are left-handed?

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A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.