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# Country A has 80 airports (must be a wealthy country!). The

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Joined: 24 Sep 2005
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Country A has 80 airports (must be a wealthy country!). The [#permalink]  10 Feb 2007, 03:39
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Country A has 80 airports (must be a wealthy country!). The distances between any two airports are not the same. Every airplane taking off from an airport flies to the nearest airport. All of the following can be the number of airplanes arriving at any airport, EXCEPT:

A. 2
B. 3
C. 4
D. 5
E. 6
Senior Manager
Joined: 04 Jan 2006
Posts: 280
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Kudos [?]: 20 [0], given: 0

Re: PS a weird net of airports [#permalink]  10 Feb 2007, 06:43
laxieqv wrote:
Country A has 80 airports (must be a wealthy country!). The distances between any two airports are not the same. Every airplane taking off from an airport flies to the nearest airport. All of the following can be the number of airplanes arriving at any airport, EXCEPT:

A. 2
B. 3
C. 4
D. 5
E. 6

Interesting question.

I am not really sure how to deal with this question. But, it may relate to the hexagonal network that all the distances between spot are the same. The number of airplanes arriving at any airport will be 6.

If the distance is not the same, 6 is impossible. So the answer is E?
Director
Joined: 26 Feb 2006
Posts: 905
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Re: PS a weird net of airports [#permalink]  10 Feb 2007, 08:49
laxieqv wrote:
Country A has 80 airports (must be a wealthy country!). The distances between any two airports are not the same. Every airplane taking off from an airport flies to the nearest airport. All of the following can be the number of airplanes arriving at any airport, EXCEPT:

A. 2
B. 3
C. 4
D. 5
E. 6

go with E. since the distance between two airports are not the same, the maximum number of airports that can be equidistance in a circular way is 6, which is not possible. therefore, it is 6.
Senior Manager
Joined: 04 Jan 2006
Posts: 280
Followers: 1

Kudos [?]: 20 [0], given: 0

Re: PS a weird net of airports [#permalink]  10 Feb 2007, 12:00
amorpheus wrote:
devilmirror wrote:
laxieqv wrote:
Country A has 80 airports (must be a wealthy country!). The distances between any two airports are not the same. Every airplane taking off from an airport flies to the nearest airport. All of the following can be the number of airplanes arriving at any airport, EXCEPT:

A. 2
B. 3
C. 4
D. 5
E. 6

Interesting question.

I am not really sure how to deal with this question. But, it may relate to the hexagonal network that all the distances between spot are the same. The number of airplanes arriving at any airport will be 6.

If the distance is not the same, 6 is impossible. So the answer is E?

Why hexagonal only why not octagonal?

Draw 2 circles. The first circle has a regular hexagon inside. The other has a regular octagonal.

In the first circle, the distance of each side of hexagon is equal to radius of the circle.

In the second circle, the distance of each side of octagonal is shorter than the radius.

On my assumption, I try to find a picture that every dot on the network must have the same distance. Only hexagonal shape can create such condition.
Re: PS a weird net of airports   [#permalink] 10 Feb 2007, 12:00
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