|California State Capital dome (2/2007)|
Here's a question like that.
It involves trying to figure out the best place to live between different locations. You can think about it as trying to find the place that's nice and quiet--and maximally far from big city centers (the "blast zones"). Or you can think of this question as trying to find a place that minimizes the distance you have to travel to the city centers.
Imagine it this way: Suppose you have 4 cities that you want to visit regularly. Say, the capitals of California, Washington, Montana, and Nevada. (If you want, imagine that you have franchise businesses--or family members--in each of those locations and need to visit each place once a month. How can you minimize travel time between the locations? To simplify the problem, assume you'll drive from place to place.)
This gives us our question for the week:
1. Can you find the place that's "in the middle" of all four cities? (The capitals given above.) That is, find the place you'd like to live that's equidistant from all four city centers. (Feel free to ignore curvature of the Earth effects.)
Obviously, there's not a simple query that's going to solve this for you.
You'll have to step back and ask, "How CAN I solve this problem?"
Hint: You're probably going to use a map... but how?
I'll give another hint tomorrow (along with some thoughts about collections).
When you post your solution, be sure to say HOW you figured it out. (Just sticking a pin in the map roughly in the middle isn't the kind of solution I'm looking for...)
For today, enjoy thinking about this research Challenge!