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..
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Can all letters of the alphabet be represented using only a 5 by
5 array of cubes ?
Is it possible to create every combination of three
letters in a 'perforated cube' ?
What difference does the orientation of the letters make ?
How many ways are there to orientate three non-symmetric letters
such as F, J and P ?
What difference will it make to use letters that have symmetry
of some kind ?