[Fsf-friends] Four Friends - Part I

[Anand Babu]

,----[ Ramanraj K <ramanraj.k@gmail.com> ]
| 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?
`----

 Task                             ::: Time taken in minutes
 ----------------------------------------------------------
 1 and 2  take torch and walk across : 2
 1 returns with torch                : 1
 10 and 5 walk across with the torch : 10
 2 returns  with torch               : 2
 1 and 2 cross with the torch        : 2
 ----------------------------------------------------------
 Total time:                      ::: 17 minutes

-- 
Anand Babu 
GPG Key ID: 0x62E15A31
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