[Fsf-friends] Four Friends - Part I

Ramanraj K ramanraj.k@gmail.com
Sun Aug 7 13:41:40 IST 2005

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?

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