Not logged in.   Log in
From the people behind the Alan Turing Cryptography Competition.
Home Register FAQ Rules For Teachers News Leaderboard Forum Archive

Puzzle 4

Two television executives are discussing their plans for the next hit TV reality show: 'Strictly The Great British Celebrity Zombie Island - Get Me Out of Here!'

"There's an infinite number of Z-list celebs who want to appear on TV to revive their flagging careers - and viewers love watching them suffer!" said Django.

"And zombies are really popular! And we just happen to have one!" said Pandora.

"So here's the format", continued Django. "We've got a small tropical island. The centre of the island is impenetrable with just an extremely narrow beach around the coastline. The coastline is exactly 1,200m long."

"We'll put the zombie and the celeb down on opposite sides of the island: they'll start 600m apart", said Pandora.

"But celebs - even Z-list ones - can easily outsmart a zombie. So we'll have to tie them down so they can't move. How fast can your zombie shuffle?" asked Django.

"Surprisingly quickly", said Pandora. "It can cover 100m each minute. It's not bright enough to turn around though. Each minute it shuffles either 100m forwards or 100m backwards around the coastline. It goes forwards 2/3rds of the time and backwards 1/3rds of the time, independently of how it has already moved."

"So eventually - we hope! - the zombie will reach the celeb..." said Django.

"...and then eats their brains. At which point there's a 3-minute commercial break and then we start again with a new celebrity", said Pandora.

"This programme has got to make us money though", said Django, thoughtfully. "We need to know the average amount of time between commercial breaks!"

You should calculate the average amount of time, in minutes, between the start of consecutive commercial breaks, correct to 2 decimal places (for example, if you think the answer is five minutes and fifteen seconds enter 5.25).

Your answer:
No answers can currently be submitted as the competition is closed.
MathsBombe Competition 2019 is organised by the The School of Mathematics at the University of Manchester.
© The University of Manchester 2012–2019, All Rights Reserved
Contact us | Privacy notice