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How many winning lines can you make in a three-dimensional version of noughts and crosses?

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

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How many different symmetrical shapes can you make by shading triangles or squares?

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A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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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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If you move the tiles around, can you make squares with different coloured edges?

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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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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 game for 2 or more people, based on the traditional card game Rummy.

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A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Why not challenge a friend to play this transformation game?

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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?