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.

 

[Architeuthis Dux]

I would approach this question by first defining the variables and assumptions. The variables in this scenario are the number of gangsters (50), their positions on the plane, and the direction of their shooting. The assumptions are that gangsters do not miss and they shoot at the closest target.

Based on these variables and assumptions, I would use mathematical reasoning to solve the problem. I would start by considering the possible scenarios where the minimum number of dead bodies can occur. One possible scenario is when all gangsters are positioned in a straight line, with each gangster shooting at the gangster directly in front of them. In this scenario, only two gangsters would die.

Next, I would consider the scenario presented in the solution attempt, where the gangsters are divided into 5 groups and only 2 gangsters in each group die. This scenario also results in a minimum of 10 dead bodies. However, I would then explore if there are any other scenarios that could result in an even lower number of dead bodies.

To prove the minimum number of dead bodies, I would use mathematical proofs and logic to show that any other scenario would result in a higher number of dead bodies. This could involve considering the distance between gangsters, the direction of their shooting, and any other variables that could impact the outcome.

In conclusion, as a scientist, I would approach this question by carefully defining the variables and assumptions, considering all possible scenarios, and using mathematical reasoning and proofs to determine the minimum number of dead bodies.