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# What is the maximum number of points that can be placed on a circular

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What is the maximum number of points that can be placed on a circular  [#permalink]

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04 Jun 2020, 03:21
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75% (hard)

Question Stats:

38% (01:49) correct 62% (01:51) wrong based on 61 sessions

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What is the maximum number of points that can be placed on a circular disk of radius 1 meter (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 meter from each other.

A)9

B)8

C)6

D)5

E)7

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Re: What is the maximum number of points that can be placed on a circular  [#permalink]

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04 Jun 2020, 05:16
4
1
To fit in as many points as possible, we'll want them to be as close together as possible, so (if we can) we want to make the distance between points 1 meter. Along a diameter, we can place three points -- one at the center, and two on the circumference. If we have a point at the center, every other point will need to be on the circumference, to be 1 meter away from the center.

So now we want points around the circumference that are 1 meter apart, in a straight line. If you take two consecutive points around the circumference, if they're 1 meter apart, and the radius is 1 meter, you'd make an equilateral triangle by connecting the two circumference points and the center. So there will be a 60 degree angle at the center, and going around the circle, you'll be able to place 6 points around the circumference that are 1 meter apart in a straight line (since 6*60 = 360). Including the center, we have 7 points in total.
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##### General Discussion
Senior Manager
Joined: 18 Dec 2017
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Re: What is the maximum number of points that can be placed on a circular  [#permalink]

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04 Jun 2020, 07:36
4
Circumference of the circle =2×3.14×1
= 6.28
So 6 points on the circle and one at center total 7

Posted from my mobile device
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Joined: 22 Mar 2020
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What is the maximum number of points that can be placed on a circular  [#permalink]

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05 Jul 2020, 00:48
IanStewart wrote:
To fit in as many points as possible, we'll want them to be as close together as possible, so (if we can) we want to make the distance between points 1 meter. Along a diameter, we can place three points -- one at the center, and two on the circumference. If we have a point at the center, every other point will need to be on the circumference, to be 1 meter away from the center.

So now we want points around the circumference that are 1 meter apart, in a straight line. If you take two consecutive points around the circumference, if they're 1 meter apart, and the radius is 1 meter, you'd make an equilateral triangle by connecting the two circumference points and the center. So there will be a 60 degree angle at the center, and going around the circle, you'll be able to place 6 points around the circumference that are 1 meter apart in a straight line (since 6*60 = 360). Including the center, we have 7 points in total.

you can't put a point on the center of a disc as in the center there is simply a hole
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Re: What is the maximum number of points that can be placed on a circular  [#permalink]

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05 Jul 2020, 02:36
robinbjoern wrote:
IanStewart wrote:
To fit in as many points as possible, we'll want them to be as close together as possible, so (if we can) we want to make the distance between points 1 meter. Along a diameter, we can place three points -- one at the center, and two on the circumference. If we have a point at the center, every other point will need to be on the circumference, to be 1 meter away from the center.

So now we want points around the circumference that are 1 meter apart, in a straight line. If you take two consecutive points around the circumference, if they're 1 meter apart, and the radius is 1 meter, you'd make an equilateral triangle by connecting the two circumference points and the center. So there will be a 60 degree angle at the center, and going around the circle, you'll be able to place 6 points around the circumference that are 1 meter apart in a straight line (since 6*60 = 360). Including the center, we have 7 points in total.

you can't put a point on the center of a disc as in the center there is simply a hole

I don't know how to react to this.
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Re: What is the maximum number of points that can be placed on a circular  [#permalink]

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05 Jul 2020, 02:46
gurmukh wrote:
Circumference of the circle =2×3.14×1
= 6.28
So 6 points on the circle and one at center total 7

Posted from my mobile device

I don't think the argument (highlighted) is justified. The circumference is an arc, and you want them away 1 meter on a straight line. So in my opinion we cannot draw this conclusion. If we take IanStewart 's method above of drawing equilateral triangles, that makes much more mathematical sense. What do you think?
Re: What is the maximum number of points that can be placed on a circular   [#permalink] 05 Jul 2020, 02:46