Question involving some reasoning.

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SUMMARY

The problem involves fifty gangsters positioned on a plane, each shooting at the closest gangster simultaneously. The conclusion drawn from the discussion is that the minimal number of dead bodies is ten, achieved by grouping the gangsters into five circles where only the two central gangsters in each circle are killed. This solution is based on the assumption that gangsters shoot the closest target, leading to a strategic arrangement that minimizes casualties.

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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.
 

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

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