The squashed bee Two trains set off from Oxford and London, a distance of 60 miles. The trains are heading directly towards each other, each chugging along at 60 mph. A bee is sitting on the front of the Oxford train and flies at 120 mph to the front of the London train. It keeps flying backwards and forwards between the two trains until they collide and the bee is squashed.

The Puzzle: How far did the bee fly?

StumbleUpon Toolbar Stumble It!
Hints and solutions below:

Hints will appear here!

If you have too much mathematical training, you may initially take an unnecessarily complicated approach. This problem requires only a very simple calculation.

Think about this question instead: how long does it take for the trains to meet?

The trains are heading to each other at a combined speed of 120 mph. At a distance of 60 miles, they take half an hour to meet. The bee is flying at 120 mph so the total distance it travels in half an hour is 120 × 0.5 = 60 miles.

The more complicated solution I alluded to in Hint 1 involves summing the infinite series of distances between each change of direction the bee makes.

A (probably apocryphal!) tale relates to an occasion when Norbert Wiener (a great mathematician at MIT) was told this riddle. Of course, Wiener came up with the solution immediately. The student who asked him the question remarked that when a mathematician is given the problem, he will usually solve it by summing the infinite series. To which Wiener replied, "Oh, I did."

Logic Puzzles:

The Twelve days of Christmas (*/**) 1 Dec 07
How many gifts did my true love send me?
The squashed bee (**) 15 Oct 07
How far does the bee travel before it's squashed?
12 coins (****) 14 Oct 07
Find the counterfeit coin in 3 moves
Black and blue socks (*) 28th Aug 07
Choose a matching pair of socks in the dark
100 monks (**) 18th Aug 07
How do you communicate simply by not dying?
Coins on a table (***) 15 Aug 07
The last person to place a coin wins
10 Barons (***) 15 Aug 07
Help me catch a cheating Baron by weighing gold bars
Fox, chicken, grain (*) 14 Aug 07
Cross a river taking only one at a time
5 pirates (****) 14 Aug 07
A tricky problem in booty allocation
Try our other Puzzles:

50 states
Our popular 50 states name game.
England counties
Name the 48 ceremonial counties of England.
53 countries and territories of Asia.