Visualising and representing

problem
Favourite

Bendy Quad

Age

14 to 16

Challenge level

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
problem

Platonic Planet

Age

14 to 16

Challenge level

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
problem

A Problem of Time

Age

14 to 16

Challenge level

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
problem

AMGM

Age

14 to 16

Challenge level

Can you use the diagram to prove the AM-GM inequality?
problem

A Tilted Square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Favourite

Hexy-Metry

Age

14 to 16

Challenge level

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

Far Horizon

Age

14 to 16

Challenge level

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
problem
Favourite

Mixing More Paints

Age

14 to 16

Challenge level

Can you find an efficent way to mix paints in any ratio?
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Favourite

Dating Made Easier

Age

14 to 16

Challenge level

If a sum invested gains 10% each year how long before it has doubled its value?
problem
Favourite

Funnel

Age

14 to 16

Challenge level

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?