
Visualising and representing
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problemShow that among the interior angles of a convex polygon there cannot be more than three acute angles.
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problem
Three by one
There are many different methods to solve this geometrical problem - how many can you find?
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problem
Hexy-metry
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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problem
Corridors
A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner. -
problem
Counters
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? -
problem
Make 37
Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?
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problem
Königsberg
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
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problem
Shady symmetry
How many different symmetrical shapes can you make by shading triangles or squares?
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problem
Pick's theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
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problem
Take three from five
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?