Passing ships in the night

[Badger]

You are taking a cruise from Liverpool to New York City.The passage takes an hour less than 7 days (167 hours) and then the ship is in port 23 hours before returning. The cruise line has ships which depart from NYC and Liverpool every day of the week at precisely 10:00 GMT. The ships all sail along the same route so as you make the passage, you will pass by other ships from the cruise line traveling in the opposite direction.

How many of the cruise line's ships will you pass by going in the opposite direction while making this voyage ?


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[tcm]

13!

It seems like the answer should be 7 BUT after you have just departed there are 7 ships which are traveling towards you. You will pass them and the 6 which leave as you are at sea. Since the ships leave at the same hour from each direction every day then you will pass a ship every 1/2 day.

It also might seem that the answer is 12 (and not 13) because a minute away from the dock on the voyage there are 7 ships heading towards us. The 7th left the dock on the other side at the same time that we did. Since the trip takes almost 7 days, another 6 ships will leave the dock before we arrive.

It also might seem that the answer is 14 (instead of 13) because the passage takes "an hour less than 7 days". If the passage took exactly 7 days (7 * 24 hours) then you could argue 13, 14, or 15 crossings depending on whether you thought that the ship arriving "crossed" the one departing even though they dock and un-dock at the exact same instant in time. If it takes 1 hour less than 7 days, then you pass a ship after ~0.5 days, ~1 day, ~1.5, ~2, ~2.5, ~3, ~3.5, ~4, ~4.5, ~5, ~5.5, ~6, and ~6.5 days but not after 7 days because your ship gets in an hour before the next ship departs.

Hurrah!

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[Badger]

TCM does it again

A very detailed correct answer takes TCM to the Scuttlebutt Mastermind Trophy. (That's enough brain teasers for now.)

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[BlueSkyNick]

Re: TCM does it again

(That's enough brain teasers for now.) - Thank God for that !


<hr width=100% size=1>I'm average size, Its just that everybody else is short.

 

[paulrossall]

Re: TCM does it again

If one assumes TCM is live on these forums 24/7 (as he seems to be), it should be pointed out that he took almost 10 hours to work the answer out!! Next time perhaps you should give at least one days notice before you pose the question so a proper competition can be held to see who responds correctly fastest.

<hr width=100% size=1>" there is nothing-absolutely nothing-half so much worth doing as simply messing about in boats".