This could be too difficult:



You are given an elliptical-shaped land and you are asked to choose n arbitrary points on its boundary. Then you connect each point with every other point using straight lines, forming n(n - 1)/2 connections.

What is the maximum number of pieces of land you will get by choosing 'n' points on the boundary carefully?

Here are some sample answers:
n=1 Pieces=1
n=2 Pieces=2
n=3 Pieces=4
n=4 Pieces=8


The diagram shows the division of land at n=6,

10 comments:

  1. Sambhav GuptaJanuary 26, 2011 at 6:12 PM

    if the answer is 2^(n-1), i didn't find it too difficult

    ReplyDelete
  2. AnujJanuary 26, 2011 at 6:34 PM

    it IS too difficult. i used a computer to solve it... :)

    ReplyDelete
  3. AnonymousJanuary 26, 2011 at 11:59 PM

    (n^4 - 6n^3 + 23 n^2 -18n)/24 + 1
    5-->16
    6-->31
    7-->57
    8-->99
    9-->163

    ReplyDelete
  4. akash rupelaJanuary 27, 2011 at 12:01 AM

    I m gettin the same answer

    ReplyDelete
  5. Tushar SinglaJanuary 27, 2011 at 9:03 AM

    2^(n-1)...same...

    ReplyDelete
  6. AnujJanuary 27, 2011 at 10:08 AM

    wow! someone got the right answer!

    ReplyDelete
  7. akash rupelaJanuary 27, 2011 at 4:42 PM

    and the good thing is that C0+C2+C4 equals 2^(n-1) only for n<=5

    ReplyDelete
  8. AnujJanuary 27, 2011 at 7:02 PM

    who marked this question 'too easy'?

    ReplyDelete
  9. AnonymousJanuary 29, 2011 at 5:57 PM

    Tushar, If I know C++, I have a right to use it.
    Isme shak vali kya baat hai?

    ReplyDelete
  10. aakashFebruary 21, 2011 at 6:16 AM

    it is a 4th level AP

    answer is 1+(n-1)C0+(n-1)C1+(n-1)C2+
    (n-1)C3+(n-1)C4

    CHECH IT OUT

    ReplyDelete

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