Le Havre to New York

Le Havre to New York
A lot of tech companies and other employers seem to have a penchant for asking tricky questions for potential candidates to assess how they think. In some cases, there is no right answer per se, it's rather a way of assessing how your brain is wired. This week's brain teaser incorporates 18th-century French mathematician Édouard Lucas. The story goes like this...

Lucas was attending a science conference, and after lunch, several noted mathematicians were standing around. Lucas spoke up and challenged them to the following puzzle. A few guessed wrong, most remained silent, and no one answered correctly.


Every day at noon an ocean liner leaves Le Havre to sail for New York, and (simultaneously) an ocean liner sails from New York to Le Havre. The crossing takes exactly seven days and seven nights in either direction. How many other ocean liners will an ocean liner leaving Le Havre today pass at sea before arriving in New York?


If you're wondering whether a ship casting off from harbor just as another arrives counts as a "pass at sea," yes, the solution does count these encounters. We suggest you use a pen and a piece of paper to visualize all the ship crossings. Remember that the correct answer will include all the ships that are already at sea when the target ship sets sail.



The correct answer is 15 ocean liners. When one sets sail from Le Havre, there are 6 other ocean liners already at sea that set out from New York. In addition to these, 7 more ocean liners will leave New York during the voyage, including the ship that leaves simultaneously from New York as our ship casts off from Le Havre. So, a ship leaving Le Havre "today" will see 13 other ships in the ocean. In addition to these, it will cross paths with another ship as it casts off from Le Havre, and yet another as soon as it arrives in New York, adding 2 more. An ocean liner leaving Le Havre on any given day will pass 15 other ocean liners on its way to New York.

Still confused?

This diagram will help explain what is going on in the story. 

The diagram above demonstrates a 30-day month and each line represents an ocean liner. Blue lines are casting off from Le Havre, and red lines are casting off from New York. If we suppose that the ship leaving "today" is leaving on the 7th of the month, you can see that it encounters 15 other ocean liners during its 7-day journey.

Share your thoughts online.


Did you guess last week's brain teaser? 

3 Switches, 1 Light Bulb