Wednesday, June 2, 2010

The Lantern and the Bridge

A small family is being pursued by an unknown enemy in the middle of a dark, dark night.  It comes to a deep chasm spanned by a narrow bridge. 

The family is composed of a father, mother, grandfather, and child.  The father is athletic and can cross the bridge in 1 minute; the mother can cross in 2 minutes; the child can cross in 5 minutes; and the grandfather, the slowest, takes 10 minutes to cross.  They have a lantern with them. 

Since it's pitch dark, the bridge can't be crossed without the lantern.  The bridge is so narrow that only two can cross at a time, and each pair can only move as quickly as its slowest member. 

Their pursuer is likely not far behind.  What is the quickest way to get everyone across the bridge?









Solution:
They can all get across in 17 minutes.  Thanks to Rob Strong for articulating the solution. 

F&M cross: 2 min
F returns: 1 min
GF&C cross: 10 min
M returns: 2 min
F&M cross again: 2 min.

4 comments:

  1. I'm thinking...father and grandfather cross together, father runs back, child and father cross together, father runs back, father and mother cross together.
    This will take 19 minutes total, but I'm not completely positive about my answer...

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  2. Slight improvement:

    F & M cross: 2 min
    F returns: 1 min
    C & GF cross: 10 min
    M returns: 2 min
    F&M cross: 2 min

    Total: 17 minutes

    Still not certain that's the best possible answer, though.

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  3. Nick Guthrie (Dad)June 23, 2010 at 6:30 AM

    I thought of same ans. as Anthony. I didn't reply because that seemed too simple and I couldn't think of an other way. Later I glanced at Rob's solution. I thought "How clever to send 2 slowest together" but then thought that did not help because 2nd slowest would have to return. I hadn't noticed Mom has there from 1st trip to make the return almost as fast as Dad. CLEVER!

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  4. Also 17 minutes but different order:
    F&M cross: 2 min
    M returns: 2 min
    GF&C cross: 10 min
    F returns: 1 min
    F&M cross again: 2 min.

    ReplyDelete