Enigma 1274: Going for a walk
1 December 2014
Posted by on
From New Scientist #2432, 31st January 2004
George is planning a walking holiday on a long distance footpath that runs generally north-south. He will start at a village near the middle and toss a coin to decide whether to walk north or south. He will then walk in that direction to the next village and check in at the local inn.
Each morning he will toss his coin to decide whether to walk north or south and, as on the first day, walk in that direction to the next village.
Fred commented that George might see the same scenery several times, and might finish anywhere after his planned number of days.
“Well, not quite anywhere, but there are quite a number of possibilities. I might finish where I started.”
“What is the chance of that happening?”
“Exactly 95 per cent of what it would have been if my holiday had of been two days shorter.”
What, as a fraction in its lowest terms, is the probability of George finishing where he started?