Nantes to New York

Originally formulated by the French mathematician Édouard Lucas, this maths-infused riddle is a tough one, but you can make it much easier by writing parts of it down, as you’ll soon find out.

At 12:00 noon, every day, an ocean liner leaves the French port of Nantes, heading to New York. At that exact moment, an ocean liner leaves New York for Nantes. The crossing always takes 7 days and 7 nights, in both directions.

How many other ocean liners will an ocean liner leaving Nantes cross paths at sea before it arrives in New York?

Note: One ocean liner leaving as soon as one arrives counts as ‘crossing paths at sea’.

Show Answer

The answer is 15 ocean liners. When a liner sets sail from Nantes, there are 6 others at sea who set out from New York. This makes 7 liners. Then, another 7 liners will leave during the voyage. Any ship leaving Nantes on the first day of the process will encounter 13 other liners at sea, but will also another liner as it casts off from Nantes, and another as it arrives at New York, which is another 2. Essentially, then, it will encounter 13 at sea and 2 at port, making 15 in total.

Try drawing out the two journeys between the ports and you’ll see!

 

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