Maths Week Challenge 5 – The Lightbulb

16 Oct 2015

It’s the final day of Maths Week. All this week we’ve been bringing you Maths Week Challenges, curated in collaboration with University College Cork, currently celebrating the bicentenary of noted mathematician George Boole. For our final Challenge, we’re making things more devious than ever.

Friday’s Maths Week Challenge

At the beginning of eight seconds, a light is on and stays on for four seconds. After four seconds the light is switched off and stays off for four seconds. Then it is switched on and stays on for two more seconds. Then it is switched off and stays off for one more second. Then it is switched on and stays on for another half a second.

This pattern of on and off continues, with the time interval halving each time.

When the eight seconds have elapsed, is the light on or off?

Todays Maths Week Challenge comes courtesy of Des MacHale, Emeritus Professor of Mathematics at UCC and George Boole biographer.

Make sure to check back in tomorrow for the solution to today’s Challenge.

Solution to Friday’s challenge

Solution from Prof Des MacHale, University College Cork:

Disappointingly, the data do not determine a solution – the light may be on or off. Mathematically, the infinite sequence ‘1,0,1,0,1,0,…’, where the odd terms are 1 and the even terms are 0, does not have a limit.

Updated 2 November 2015 at 5.30pm to include the solution to the Friday Maths Week Challenge.