Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube? P is a point on the
circumference of a circle radius r which rolls, without
slipping, inside a circle of radius 2r. What is the locus The
coke machine in college takes 50 pence pieces. It also takes a
certain foreign coin of traditional design. Coins inserted into
the machine slide down a chute into the machine and a drink is
duly released. How many more revolutions does the foreign coin
make over the 50 pence piece going down the chute? N.B. A 50
pence piece is a 7 sided polygon ABCDEFG with rounded edges,
obtained by replacing AB with arc centred at E and radius EA;
replacing BC with arc centred at F radius FB ...etc.. This
problem is taken from the UKMT Mathematical Challenges.