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Degree Ceremony

Can you find the sum of the squared sine values?


Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

The Dodecahedron

Age 16 to 18
Challenge Level

DodecahedronA and B are the centres of two opposite faces of a regular solid dodecahedron.

What is the shortest distance between A and B on the surface?