Meeting point for 5 people with least distance travelled (interview question) I had an interview today and I'm completely stumped on what they asked me. Essentially: if you are given 5 people on a 2D grid, and you need to meet at a point with the least amount of distance travelled, how would you calculate it?
What I had told the interviewer after some questions is to use the pythagorean theorem for every point and then add these together. I know I completely failed in answering...
Anyway, what is the proper way to do this? And is there a name for this type of problem so I can read more into it?
Thanks!

Let's do it for a single dimension, X1 to X5 in ascending order.
X3 should be the meeting point.
If the meeting point X > X3 then you had 3 people going from X3 to X instead of 2 people from X to X3. With this principal you get that the best point is X3.  
The Y points should also be set in ascending order, which means that the person at X1 does not necessarily have to be at Y1.  
Similarly, Y3 is a good meeting point for the Y axis.  
I don't know whether X3,Y3 is the best point, but the answer is a good start for an interview.
