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?
Imagine a stack of cards, numbered one to seven in order, with
one on the top.
Discard the top card (card 1) and put the next card
(card 2) to the bottom of the stack.
Put out card 3 and then put card 4 under.
Continue putting one out and
one under until you are holding only one card - it should be
What happens if you start with 8 cards ?
What happens if you start with 9 cards ?
How much can you find out about this situation ?
Send us whatever you discover.
Continue exploring until you can predict the final card and
explain why your method works.