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.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

john will be here soon
okayy :)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

:)
here he is
have a good 1!
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
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
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
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
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
okayy ..i understand..thank you very much.. :) but how can we show it using pigeonhole principle ?
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
oh okaayyy.. thank you veryyyy much.. :) :)
No problem!

Not the answer you are looking for?

Search for more explanations.

Ask your own question