Question involving some reasoning.

[azatkgz]

Homework Statement

Fifty gangsters on a field are shooting each other simulteneously.Assume that
i.Gangsters are points on the plane.
ii.Gangsters don't miss,so once he shoots at someone,the target is killed.
iii.Each gangster shoots the one that is closest to him(or any of the closest ones if they are on same distance from him)

What is the minimal number of dead bodies?They shoot each other just once,all fifty at the same moment.Guess the answer and then try to prove it.

The Attempt at a Solution

I divided 50 gansters to 5 groups.In each group only 2 gansters in the center of circle are dying(see picture).With arrows I showed direction of shooting.So my answer is only 10 gansters.

 

[wildman]

I'm no mathematician but it looks good to me.