Arvind, an old friend of mine, recently told me this story:
One night, four travellers named One, Two, Five and Ten walking through a forest, come to a deep gorge and find that they have to continue their journey across a weak wooden bridge, that won't stand the weight of more than any two of them at a time. The bridge has a few missing logs and they had only one torch with them to guide them across. Also, One takes 1 minute, Two takes 2 minutes, Five takes 5 minutes and Ten takes 10 minutes to cross the bridge, due to their individual abilities. What is the minimum time within which the four friends could cross the bridge?
I reasoned that One being the fastest, could take Two, Five and Ten across in about 19 minutes as follows:
Task ::: Time taken in minutes ---------------------------------------------------------- 1 and 10 take torch and walk across: 10 1 returns with torch : 1 1 and 5 walk across with the torch : 5 1 returns with torch : 1 1 and 2 cross with the torch : 2 ---------------------------------------------------------- Total time: ::: 19 minutes
Arvind said that they could save two minutes with another plan. I was sure there is a "catch" somewhere, because it appeared impossible. Did 1 and 2 cross earlier, and did 2 throw the torch from the other side? No, there are no catches, it is a purely logical problem to be solved just the way I proposed, but his plan would take two minutes less of time. How could they cross the bridge in just 17 minutes?