Rabbit Puzzle

Replies

• 

  shalini_goel14

  Sorry , it will be sum of following series
  
  (n-1) + (n-1)(n-2) +(n-1)(n-2)(n-3)+... [(n-1)(n-2)..{n-(n-1)}]
• 

  pradeep_agrawal

  I edited the post to make question more clear.
  
  -Pradeep
• 

  Anil Jain

  shalini_goel14

  Sorry , it will be sum of following series
  
  (n-1) + (n-1)(n-2) +(n-1)(n-2)(n-3)+... [(n-1)(n-2)..{n-(n-1)}]

  I have not calculated till now... but certainly this is not the asnwer..
  
  Consider n= 1
  As per your expression, value would be 0
  
  However 1 rabit should be the value....
  
  -CB
• 

  shalini_goel14

  crazyboy

  I have not calculated till now... but certainly this is not the asnwer..
  
  Consider n= 1
  As per your expression, value would be 0
  
  However 1 rabit should be the value....
  
  -CB

  No each rabbit can give birth only in second month so for 1 month[i.e n=1] there will be 0 rabbit.
  
  PS: Correct me if wrong.
• 

  pradeep_agrawal

  shalini_goel14

  No each rabbit can give birth only in second month so for 1 month[i.e n=1] there will be 0 rabbit.
  
  PS: Correct me if wrong.

  Yep, you are wrong here. Even in the first month we have 1 rabbit (the unique rabbit who starts the chain) 😀
  
  And a rabbit can give birth after second month (i.e., start of third month). This is the clarification i have done by editing the puzzle.
  
  -Pradeep
• 

  shalini_goel14

  pradeep_agrawal

  Yep, you are wrong here. Even in the first month we have 1 rabbit (the unique rabbit who starts the chain) 😀
  
  And a rabbit can give birth after second month (i.e., start of third month). This is the clarification i have done by editing the puzzle.
  
  -Pradeep

  Ok, I got it , it is wrong. Will post later the correct answer. 😀
  
  Bye ! Keep on trying 😉
  
  PS: "Hurry makes curry" -how true 😡
• 

  RajdeepCE

  After n days the number of rabits will be n[sup]th[/sup] fibonacci number. Here is explanation,
  1st month = 1 rabit,
  2nd month = 1 rabit,(1st rabit cant give birth now)
  3rd month = 2 rabit,(1st rabit starts giving birth)
  4th month = 3 rabit,(1st rabit gives birth to another)
  5th month = 5 rabit,(both rabit start giving birth)
  So the answer will be nth element of fibonacci series.
  
• 

  Anil Jain

  And what would be n^th element ?? Thats what he is looking for.. 😀
• 

  RajdeepCE

  I mentioned that in my posts first and last line. And again after n months the number of rabits will be the n[sup]th[/sup] fibonacci number. And the equation of fibonacci series is,
  f(n)=f(n-1)+f(n-2), n=2,3,4,... & f(n-1)=f(n-2)=1.
• 

  pradeep_agrawal

  RajdeepCE

  So the answer will be nth element of fibonacci series.

  Yes that the correct answer that the number of rabbits on nth day will be the nth element of the fibonacci series.
  
  

  RajdeepCE

  And the equation of fibonacci series is,
  f(n)=f(n-1)+f(n-2), n=2,3,4,... & f(n-1)=f(n-2)=1.

  I feel you mean to say "f(1)=f(2)=1" instead of "f(n-1)=f(n-2)=1".
  
  My next query, is there any simple equation through which i can directly calculate the number of rabbits on nth day (i.e., nth element of fibonacci series) instead of going by formula
  
  f(n)=f(n-1)+f(n-2), f(1)=f(2)=1.
  
  -Pradeep
• 

  silverscorpion

  Ok. That's easy.
  
  The formula for the N[sup]th[/sup] fibonacci number is,
  
  

  {[(1+sqrt(5))/2][sup]n[/sup] - [(1-sqrt(5))/2][sup]n[/sup]} / sqrt(5)

  ie.,
  
  (1+sqrt(5))/2 is nothing but the golden ratio, 1.68. We can call it phi.
  So, Nth fibonacci number is,
  
  
  

  {phi[sup]n[/sup] - 1/phi[sup]n[/sup]} / sqrt(5);

  Am I correct??
• 

  pradeep_agrawal

  silverscorpion, not sure how you derived the formula. I tried with different value of n and i am not getting correct answers, e.g.,
  
  For n = 1, answer = 0.485
  For n = 2, answer = 1.103
  For n = 3, answer = 2.026
  For n = 4, answer = 3.506
  For n = 5, answer = 5.951
  For n = 6, answer = 10.034
  
  I am even not sure if a equation for fibonacci series exist.
  
  -Pradeep
• 

  silverscorpion

  Well, this formula exists and is quite right too. The thing is, you have to round off the answers.
  And sorry, I gave the value of phi to be 1.68. It's actually, 1.618.
  
  And another thing I forgot to mention is that, the power should actually be n+1. ie, for getting nth fibonacci number, we have to use phi[sup]n+1[/sup].
  
  So, let's calculate.
  
  For 1, we have
  
  (phi[sup]2[/sup] - 1/phi[sup]2[/sup]) / sqrt(5)
  = (1.618[sup]2[/sup] - 0.618[sup]2[/sup]) / sqrt(5) = 1.0
  
  For 2, we have
  
  (phi[sup]3[/sup] - 1/phi[sup]3[/sup]) / sqrt(5)
  = (1.618[sup]3[/sup] - 0.618[sup]3[/sup]) / sqrt(5) = 2.0
  
  Try it for other numbers too. It will work. Let me know if you got it!! 😀😀
• 

  pradeep_agrawal

  That's cool silverscorpion, this works 😀
  
  -Pradeep
• 

  silverscorpion

  I said it would!!
  
  Happy?? 😀😀
• 

  mech_guy

  Hi,
  
  Fibonacci series sum was cool indeed. I got it other way round and my answer is:-
  if n >= 3 Total no. of rabbits = 2 + [(n-2)*(n-3)/2]
  if n = 1 Total no. of rabbits = 1
  if n = 2 Total no. of rabbits = 2
  I made following sequence :-
  
  Months:- 1__2__3__4__5__6__7__8__9 ..............
  Rabbits:- _1__1__1__1__1__1__1__1__1
  __________________1__1__1__1__1__1
  _____________________1__1__1__1__1
  ________________________1__1__1__1
  ___________________________1__1__1
  ______________________________1__1
  _________________________________1
  ----------------------------------------
  Total rabbits after n months:- 1 + 1 + (1 +2 + 3 + 4 + 5 + 6 + 7 + ....(n-2) terms)
  = 2 + SIGMA(n on (n-2) terms)
  = 2 + [(n-2)*(n-3)/2] => assuming n>=3 else total = 1 for n = 1 and total = 2 for n = 2
  
  Thanks
  
  PS: my first post, didnt knw how to properly type, so using lots of underscores, hope its comprehendible.
• 

  pradeep_agrawal

  That was also a good try mech_guy. But the formula that you have given works correctly till n = 6. When we have n = 7:
  
  Total no. of rabbits = 2 + [(7-2)*(7-3)/2]
  = 2 + [5*4/2]
  = 2 + 10
  = 12
  
  But the actual answer is for n = 7 should be 13.
  
  - Pradeep
• 

  mech_guy

  Hi Pradeep,
  
  Formula for SIGMA (1 + 2 + 3....+ n) should be = n*(n+1)/2 while i did calculation for n*(n-1)/2 and that is why got wrong Total.
  
  So total should be 2 + [(n-2)*(n-1)/2]
  
  For n = 7, total number of rabbits after 7 months = 17 (how 13?)
  
  Regards
• 

  silverscorpion

  This is not correct. Using this formula, you get the series,
  
  1, 2, 3, 5, 8, 12, 17, 23, 30,...
  
  This is not fibonacci series.
• 

  mech_guy

  Hi SilverScorpion,
  
  Agreed its not a Fibonacci series.
  And yes my solution is wrong, i messed it up after 6 month onwards. It was a bad try.
  
  Regards
• 

  silverscorpion

  mech_guy

  Hi SilverScorpion,
  
  Agreed its not a Fibonacci series.
  And yes my solution is wrong, i messed it up after 6 month onwards. It was a bad try.
  
  Regards

  
  You tried!! That is great in itself!!
  
  And now you know the answer! So, enjoy!😁