Question

All the stars heros sensi champions and other great ppl.. try this
a tough one
a rod is divided into 4 parts.. what is the the probability that the parts constitute a quadrilateral?
especially for people like dalvoron,satellite,ishaan,joe,myininimya,and the other great ppl.. lol

Answer 1

truthfolly i just have the answer.. i dont have the solution too

Answer 2

what do you mean by quad please explain a little : )

Answer 3

lol! ishaan a quadrilateral of course!!!! not a square

Answer 4

For a quadrilateral, each length has to be less than the sum of the other 3 lengths, i.e. \(a<b+c+d\). No piece of the rod may therefore be greater than half the full length of the rod.

Answer 5

ya i agree

Answer 6

So we rule out the cases where 3 cuts appear in one half of the rod.

Answer 7

yes agreed

Answer 8

The probability that 3 cuts appear in the left half of the rod is \(0.5\times0.5\times0.5=0.125\), likewise for the right half of the rod.

Answer 9

wait
how is it 0.5*0.5*0.5???????????

Answer 10

So at most, the odds of the 4 parts constituting a quad is 0.75. A middle piece may be greater than half the length of the rod also though...

Answer 11

Cut 1 has a 0.5 chance of being in the left part of the rod. Cut 2 has a 0.5 chance, Cut 3 has a 0.5 chance. The chance that all 3 are in the same half therefore is the product of those 3 probabilities.

Answer 12

ok

Answer 13

I think I'm going about it the wrong way though, because a piece of 1/2 rod may exist anywhere along the length. Need to find the probability that the distance between any adjacent cuts is greater than 1/2 the rod length.

Answer 14

The answer isn't 0.5 is it?

Answer 15

BINGO

Answer 16

how did you do it???????????????????????????????????????????????????????????????????????????????????

Answer 17

Hah, boom. Not exactly sure why that's the answer. I think you'd need to do an integral to prove it. I just figure there's a 1/2 chance that at least half the rod will be intact.

Answer 18

nice guess sir.. i still want the solution though...

Answer 19

Dalvoron\?

Answer 20

Working on it...

Answer 21

ok

Answer 22

Nah, I'm stumped. Integration was never my strong point.

Answer 23

actually you do not need integration for this problem, but as i recall it is a bear

Answer 24

plz help satellite!!

Answer 25

Maybe an addition series that approximates to 0.5?

Answer 26

Or tends towards it, or whatever.

Answer 27

i have seen this for a triangle, but there it is just in two dimensions. here you are in three.

Answer 28

so it is going to be a volume problem rather than an area one. hold on

Answer 29

I assumed it was in one dimension. Things just got harder.

Answer 30

did you first do the triangle problem?

Answer 31

Never did a triangle problem. I did a similar stick based problem by Richard Wiseman before, but it didn't help much http://richardwiseman.wordpress.com/2011/01/07/its-the-friday-puzzle-93/#comments

Answer 32

answer their is easier to come by. i think we can cheat if we want, because this is a pretty standard problem. i am not sure i am up to it but the idea will have some sort of region in it

Answer 33

god but do i love the internet. if they had had this when i was in school i would have had 5 degrees by now

Answer 34

Hah, nice.

Answer 35

answer is worked out there, but i would recommend starting at problem 2 first so the idea is more clear. your answer is #4

Answer 36

Well got to go to work now anyway. I'll come back to this later.

Answer 37

oh and if you keep reading it gets better

Answer 38

much much better. so perhaps we go to the end an mimic the "simple proof' for the case n = 4

Answer 39

yes so what is the non probability proof?

Answer 40

satelite? you there?