All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
A geometric gangster shooting (Posted on 2019-05-06) Difficulty: 3 of 5
Ten gangsters are standing on a flat surface, and the distances between them are all distinct. Suddenly, each of them fatally shoots the one among the other nine gangsters that is the nearest. What is the maximum possible number of surviving gangsters?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
A guess (spoiler?) | Comment 1 of 6
I guess that it is possible for 7 to survive.

First, 6 survivors is easy.  

One way:  8 men stand at the corner of two almost-squares, widely separated.  one man stands in the center of each almost-square.  All corners shoot at the center men, and the center men each shoot at a corner.  6 survive.

Alternatively, 5 men stand at the corner of an almost pentagon and 3 stand at the corners of an almost-equilateral-triangle, with the two widely separated.  One man stands in the center of each.

7 survivors is, I suspect, difficult but possible.  I would try placing 7 men at the corners of an almost-heptagon.  I guess that three men can be placed in the center such that the 7 corners all survive and the 3 center men all die.  one center man is placed so that it is closed to three corners, another so that it is closest to the next three corners, and the last so that it closest to the last corner.  The three center men need to be close enough so that they all shoot each other.  I have not actually done this.

I do not believe 8 survivors is possible.  I have tried using an almost-hexagon with two men in the center, but this seems to fail.

  Posted by Steve Herman on 2019-05-06 10:51:31
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information