thinking

This weekend I heard a good mathy puzzle from George Miller.  Here’s a version I found online, attributed to Howard Lederer:

You’re on a government ship, looking for a pirate ship.  You know that the pirate ship travels at a constant speed, and you know what that speed is.  Your ship can travel twice as fast as the pirate ship.  Moreover, you know that the pirate ship travels along a straight line, but you don’t know what that line is.  It’s very foggy, so foggy that you see nothing.  But then!  All of a sudden, and for just an instant, the fog clears enough to let you determine the exact position of the pirate ship.  Then, the fog closes in again and you remain (forever) in the thick fog.  Although you were able to determine the position of the pirate ship during that fog-free moment, you were not able to determine its direction.  How will you navigate your government ship so that you will capture the pirate ship?

If you wanted, you could give a convincing but math-lite answer to this.  But you can also do better, so I’m going to ask my own version of the question:

Using your answer to the above question, what is the longest amount of time that may pass from the instant you saw the pirate ship until you capture it?  Suppose the pirate ship travels at 1 km/minute, and you first see it 3 km away.  How many minutes, at most, until you capture it?

I’ll post my answer on Friday (in 5 days).

Tags: math, puzzle

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