Main content

Puzzle for Today

Puzzle No. 356 – Wednesday 14 November

Last week we learned that Cyprus now only has a fertility rate of 1 child per woman. The average Cypriot has a life expectancy of 80 years, and the population is currently evenly distributed in terms of age and gender. How long will it take for the population of Cyprus to decrease by 10% with no migration?

Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution

Let current population = Y

Number of females = Y/2

The average number of births per year = (Y/2) x (1/80) (you can imagine that all women have their child at a given age to help arrive at this assumption)

Number of deaths per year = Y/80

Net change per year = Y/160-Y/80, i.e. -Y/160

We seek the solution to the equation -10%xY = -Yn/160 where n is the number of years.

n=16 years

More fiendish brain-teasers and quizzes on BBC Radio...