Four travelers

From Math Puzzle Wiki
Revision as of 18:30, 14 July 2013 by Oscarlevin (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Puzzle

Late one night, four weary travelers come to an old rickety rope bridge over an crocodile infested gorge. With planks missing here and there, it is not safe to cross without the group's lone flashlight. Also, the bridge does not appear to be able to support more than two people at a time.

The four travelers (oddly named John, Paul, George, and Ringo) each have a varying level of mobility. John can cross in 1 minute, Paul needs 2 minutes, George needs 5 minutes, and Ringo cannot cross in less than 10 minutes. Of course when two travelers cross the bridge, they must travel at the pace of the slower of the two.

With a horde of bloodthirsty fans not far behind the travelers, what is the shortest amount of time needed to cross the bridge? How do they do it?

Help

Hint
It can be done in less than 19 minutes.
Answer
They can cross in 17 minutes.
Solution
The trick is to have George and Ringo cross together. In order to get the flashlight back across the bridge after this, either John or Paul must be on the far side. So first John and Paul cross (this takes 2 minutes). Then John comes back (another minute, we are up to 3 now). John hands the flashlight to Ringo and George and Ringo cross (10 more minutes, for a total of 13). Paul comes back (2 more minutes, 15 total). Finally John and Paul cross again, completing the trip in 17 minutes.

See also