anonymous
  • anonymous
Consider the region shown below. It is bounded by a regular hexagon whose sides are of length 1 unit. Show that if any seven points are chosen in this region, then two of them must be no further apart than 1 unit.
Discrete Math
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@johnweldon1993
anonymous
  • anonymous
john will be here soon
anonymous
  • anonymous
okayy :)

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anonymous
  • anonymous
:)
anonymous
  • anonymous
here he is
anonymous
  • anonymous
have a good 1!
johnweldon1993
  • johnweldon1993
Oh this one seems interesting So we have a hexagon |dw:1433602194782:dw| God I hate drawing on this thing lol but regardless...work with me here
johnweldon1993
  • johnweldon1993
What if we were to draw line from the center of the hexagon to each vertex? |dw:1433602323521:dw| Also labeled the fact that each side length is 1
johnweldon1993
  • johnweldon1993
Now, if I could have drawn any better...you would see that this would actually make it so the hexagon is simply 6 equilateral triangles
johnweldon1993
  • johnweldon1993
Now it wouldnt take too much visual to realize that if we choose 7 spots...any 7 random spots...at least 1 triangle will end up with 2 of those spots in it |dw:1433602536119:dw| 1 spot for each triangle...and then we have to put another one..so it would go with another triangle that already has a spot...okay thats fine
johnweldon1993
  • johnweldon1993
Now if that is true, which it is, we can show from that that since those 2 points are within a triangle of side length 1...the distance between the two cannot be greater than 1
anonymous
  • anonymous
okayy ..i understand..thank you very much.. :) but how can we show it using pigeonhole principle ?
johnweldon1993
  • johnweldon1993
If I remember correctly, Pigeonhole just states that if you try to put X items into a container of Y partitions...and X>Y then at least 1 partition will contain more than 1 X So we kinda did that here...if there are 6 partitions here...and we have 7 spots...since 7>6 then at least 1 triangle will have more than 1 point
anonymous
  • anonymous
oh okaayyy.. thank you veryyyy much.. :) :)
johnweldon1993
  • johnweldon1993
No problem!

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