problem

### Track design

Where should runners start the 200m race so that they have all run the same distance by the finish?

problem
###
Track design

Where should runners start the 200m race so that they have all run the same distance by the finish?

problem
###
Over The Pole

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.

problem
###
Flight Path

Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.

problem
###
Rolling Inside

Weekly Problem 11 - 2007

A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.

A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.

problem
###
Running Race

Weekly Problem 13 - 2006

If three runners run at the same constant speed around the race tracks, in which order do they finish?

If three runners run at the same constant speed around the race tracks, in which order do they finish?

problem
###
Roll On

Weekly Problem 5 - 2006

How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

problem
###
Efficient cutting

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

problem
###
Air Routes

Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.

problem
###
Rollin' Rollin' Rollin'

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

problem
###
Triangles and petals

An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
different flowers?