## Sunday, June 14, 2009

### Atlantic Journey

Adventurous Travel runs a luxurious cruise line, with ships traveling between New York and Lisbon across the Atlantic. Every day at noon, a ship leaves Lisbon for New York and another leaves New York for Lisbon. The trip lasts 7 days and 7 nights. You board a New York to Lisbon ship. How many Adventurous Travel ships traveling from Lisbon to New York will you meet along your journey?

This puzzle is adapted from a puzzle invented by Edouard Lucas, nineteenth-century French mathematician.

Alin Grin said...

5

Maria said...

More than 5.
Here is a hint: imagine first that you are standing on a shore in New York and think how many ships from Lisbon you will greet. Then, think what will happen when you are moving toward these ships.

Alin Grin said...

7

Alin Grin said...
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Alin Grin said...

If the NY ship is in the harbor at noon and does not depart for 7 days and nights then each noon there will be an encounter with a ship from Lisbon. If the NY ship departs at noon then the encounters become more frequent instead of each noon there will be an encounter each noon and each midnight.During the 7 day trip from NY 7 Lisbon to NY ships will depart so there will be 7 encounters.

Maria said...

You are almost there.
But the answer is not 7.

Alin Grin said...

14 encounters. since the ship encounters not only the ship which left the destination harbor on the same noon, but also all the 7 ships which preceded and are already sailing when the ship departs.

Maria said...

You are right.
Your ship would meet 13 ships heading to New York along the journey. Additionally, you will see one ship that arrived to New York just as you were leaving and one ship that is leaving Lisbon just as you arrive there. You can count one of these two shore-touching ships as well. So, answers in the range 13-15 are correct.
Alin is catching up with Rachel...