Traveler Problem


(intense music)>>Let’s try another brainteaser. Imagine we have four travelers. Let’s call them Mr. A, B, C, and D. These four gentlemen
have to cross a bridge over a deep ravine. It’s a very dark night and
the traveler’s have but a single source of light, an old-fashion oil lamp. The light is essential for
successfully crossing the ravine because the bridge is very
old and has plenty of holes and loose boards. What’s worse is, it’s
construction is really quite weak and it’s in a dilapidated condition. It can only, at best, support
two of the men at any time. The question is, how should
the men arrange themselves to cross the bridge? The oil lamp has a limited
supply of fuel and time is running out. Now, each traveler needs a
different amount of time to cross the bridge. Mr. A is young and healthy and
needs but a minute to quickly traverse the bridge. Mr. D, on the other
hand, is an old man who recently had a hip replacement,
will need 10 minutes to get across the bridge. Mr. B and Mr. C need two minutes and five minutes respectively. And since each traveler
needs the light to cross, whenever a pair of travelers go together, it’s the slower man who
determines the total time required to make the crossing. What is the quickest time
possible for all four travelers to make it across? Now, before you start thinking
of sneaky little solutions, let me just say that no, you
cannot throw the oil lamp from one side of the ravine to the other and no, you cannot leave
the oil lamp halfway along the bridge and expect
it to cast enough light so they can all make it across. Nor, like my daughter suggested is it okay to just run off and leave
the old guy to his fate alone in the dark. So, how should all four
travelers successfully cross the bridge in the minimum total time? If we assume that there’s
only 18 minutes of fuel supply left in the lamp, can they all make it? I’m gonna let you think
about this one and post your answers in the discussion forum online. (intense jingle)

2 thoughts on “Traveler Problem

  1. A and B start and A comes back = 3 min
    C and D take off and send B back = 12 min
    A and B cross over = 2 min.
    Total is 17 minutes. 
    Are there better alternatives?

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