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Geometry Level 4

There are 17 people standing in the field in such manner that all pairwise distance between them are distinct. Each one of them carries a gun. At the sound of an alarm, each of them shoots the person nearest to them. What is the maximum number of times a person can be shot at?


The answer is 5.

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Safal Biswas by Safal Biswas , 22

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3 solutions

James Shi
Feb 18, 2014

Let person A get shot the most number of times. If person B shoots person A, the circle with center B and radius AB cannot have anyone in or on it (besides person A). If person C also shoots person A, the least measure of angle BAC is the limit of x as x approaches 60 from above 60. There are 360 degrees around person A. ⌊ 360 x ⌋ = 5 \lfloor\frac{360}{x}\rfloor=\boxed{5}

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I think this is only true when every person is assumed to be in point mass. Imagine an elephant replacing a person, 16 could be the correct answer since it is possible for all 16 people to have the elephant as the nearest object.

Cheah Chung Yin - 7 years, 3 months ago

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Yes, you could assume each person to be a point ... Or you could define the distance between two people to mean the distance between their centers, which has the same effect.

Peter Byers - 7 years, 3 months ago

not sure who someone targets if they are same distance

William Fu - 7 years, 3 months ago

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"all pairwise distance between them are distinct"

James Shi - 7 years, 3 months ago

if A is nearer to B then B is nearer to A so they can shoot one another died both at a time.

srinivasarao kakulapati - 7 years, 3 months ago

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A can be nearest to B, but B can be nearest to C (in a direction away from A for instance).

Steven Perkins - 7 years, 2 months ago
Komal Sai
Feb 21, 2014

360/60 - 1

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if there are 4 persons surrounding a person then they are at 90 degree to each other but only one person can enter that circle

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