[based on an idea from the AQA GCSE problem solving questions 2008]
two strips of card are 30cm long
one is divided into thirds
the other is divided into fifths
what are the total overall lengths for these three arrangements?
what other lengths can be made?
why must the overall lengths all be even?
establish that all but four even lengths between 30cm and 60 cm (inclusive) can be made in this way (by lining up two of the fraction marks)