## Akshay_Budhkar Group Title 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 3 years ago 3 years ago

1. Akshay_Budhkar Group Title

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

2. Ishaan94 Group Title

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

3. Akshay_Budhkar Group Title

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

4. Dalvoron Group Title

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.

5. Akshay_Budhkar Group Title

ya i agree

6. Dalvoron Group Title

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

7. Akshay_Budhkar Group Title

yes agreed

8. Dalvoron Group Title

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.

9. Akshay_Budhkar Group Title

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

10. Dalvoron Group Title

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...

11. Dalvoron Group Title

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.

12. Akshay_Budhkar Group Title

ok

13. Dalvoron Group Title

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.

14. Dalvoron Group Title

The answer isn't 0.5 is it?

15. Akshay_Budhkar Group Title

BINGO

16. Akshay_Budhkar Group Title

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

17. Dalvoron Group Title

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.

18. Akshay_Budhkar Group Title

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

19. Akshay_Budhkar Group Title

Dalvoron\?

20. Dalvoron Group Title

Working on it...

21. Akshay_Budhkar Group Title

ok

22. Dalvoron Group Title

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

23. satellite73 Group Title

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

24. Akshay_Budhkar Group Title

plz help satellite!!

25. Dalvoron Group Title

Maybe an addition series that approximates to 0.5?

26. Dalvoron Group Title

Or tends towards it, or whatever.

27. satellite73 Group Title

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

28. satellite73 Group Title

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

29. Dalvoron Group Title

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

30. satellite73 Group Title

did you first do the triangle problem?

31. Dalvoron Group Title

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

32. satellite73 Group Title

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

33. satellite73 Group Title

34. satellite73 Group Title

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

35. Dalvoron Group Title

Hah, nice.

36. satellite73 Group Title

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

37. Dalvoron Group Title

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

38. satellite73 Group Title

oh and if you keep reading it gets better

39. satellite73 Group Title

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

40. Akshay_Budhkar Group Title

yes so what is the non probability proof?

41. Akshay_Budhkar Group Title

satelite? you there?