Fibonacci Series- Counting and Recursion | |

A few weeks ago, I was having a telephonic conversation with two of
our past students currently studying in IIM-A- Avijit and Dhawal. The curious thing about this was that
Avijit was our online student whereas Dhawal was our classroom student. And I
remembered how we used to tell Dhawal and his classmates in TathaGat that
"there is a guy from Orissa who is performing better than you guys in CopyCATs."
As I think of it, it is strange that we are still so close to our students.
There is Rishu Batra, a sweet and lovable TGite, Jatin Bhagat who finally
cracked CAT after three years, the serious Chinmay Kolharkar at Great Lakes,
Himanshu Tyagi who left his job despite our warnings and didn't do well, cool
dude Maneesh Dhooper who has been completely unlucky in his last two CATs but
converted XL this year, intelligent Shruti who would choke during every test
but finally got an IIM K call, and Saurabh Chhajer of this year who scored the
highest in quant in Chhota CopyCAT but disappointed us because we know his
calibre. These are some of the ones I can think of right now but I wonder how
many evenings we have passed discussing "ye student quant ya verbal mein
kaisa hai" or "is student ko thoda aur hardwork chahhiye" or
that "ye student intelligent hai but hardwork nahin karta" and all
that stuff. Year by year, there is a growing feeling among us- TG is a family.
And although we are known as hard taskmasters and what not, we do love all our
students. We would like to keep it that way. Today's article is the culmination of discussions between Kamal and me about a particular type of problems. It is strange how when you learn a new funda and go out to find problems based on that, you slowly start uncovering so many different types of problems which can be solved through that funda. Or maybe that you solved a problem but then started looking for a better solution and suddenly remembered a long-forgotten funda, and once you started applying that funda you discovered many more such problems where you can apply it. Our discussions usually make these kinds of discoveries. One of them is here. Enjoy!- Total Gadha Books To Refer: Fibonacci and Lucas Numbers with Applications You Might Also Like: CAT CBT Club: TotalGadha's Exclusive Membership Section TathaGat: TotalGadha's CAT Classroom Coaching CAT Quant Lessons: Quant Lessons for MBA Preparation CAT Verbal Lessons: Verbal Lessons for MBA Preparation CAT Quant/DI Forum: Ask doubts related to Quant & DI CAT Verbal Forum: Ask doubts related to Verbal |

Re: Fibonacci Series- Counting and Recursion | |

Great ! the explaination of derrangement is perfect |

Re: Fibonacci Series- Counting and Recursion | |

Hi Dev, Welcome to TG. Total Gadha |

Fibonacci Series- Counting and Recursion | |

Thanks Jaya Your next task is to solve the questions asked in the article. |

Re: Fibonacci Series- Counting and Recursion | |

hi this article is very interesting . i just struck at question number 7(question on jar liquid transfer).plz give us the solution . |

Re: Fibonacci Series- Counting and Recursion | |

Sharad Just write down the composition of jars after every transfer. |

Re: Fibonacci Series- Counting and Recursion | |

tg sir still not able to apply the concept of fibonacci at question 6 and 7. plz give me a proper guideline. thanx (in advance) with regards |

Re: Fibonacci Series- Counting and Recursion | |

Hi Abhishek, You are right, the derivation above was giving S _{n - 1} and not S_{n}. Thanks for pointing out. Total Gadha |

Re: Fibonacci Series- Counting and Recursion | |

For Q.1 the ans. is 194. |

Re: Fibonacci Series- Counting and Recursion | |

Hi Jaya Your answer is indeed correct. Little explanation will be more than welcome. |

Re: Fibonacci Series- Counting and Recursion | |

I am sorry sir.Actually, i skipped a few words and misinterpreted your question.I apologize again. Regards, Subhash |

Re: Fibonacci Series- Counting and Recursion | |

a8 = 194 is the least possible value for a8. It could have other values too depending on the values of a1 and a2. Regards, Subhash |

Re: Fibonacci Series- Counting and Recursion | |

Solution to Qn3: Sn = fn+2 - f2 = (fn+1 + fn) - f2 = (fn + fn-1 + fn) - 11 = (2fn + fn-1) - 11 = (2*2995 + 1851) - 11 = 7830 Regards, Subhash |

Re: Fibonacci Series- Counting and Recursion | |

Solution to Qn2: Sn = F1^2 + Fn*Fn+1 - F1*F2 = 2^2 + 1220*(754 + 1220) - 2*4 = 4 + 1220*1974 - 8 = 4 + 2408280 - 8 = 2408276 Regards, Subhash |

Re: Fibonacci Series- Counting and Recursion | |

Hi Avijit, That is true. I think I had more fun during my CAT preparation than during my JEE preparaition. Felt like an adventure. By the way, you blog at TG Town needs your attention. Do write something. Writing is a satisfying love for life. Once you get into it, life is never the same again. Total Gadha |

Re: Fibonacci Series- Counting and Recursion | |

Dear sir, Kindly do let me know how to solve Qn6 using Fibonacci series. Regards, Subhash |

Re: Fibonacci Series- Counting and Recursion | |

Yes Subhash You are right this time. Now recheck your answer for question number 5 also. |

Re: Fibonacci Series- Counting and Recursion | |

Subhash Please go through the explanation of similar question in article and try to formulate the recursion properly. |

Re: Fibonacci Series- Counting and Recursion | |

Subhash Your recursion is correct but f |

Re: Fibonacci Series- Counting and Recursion | |

Hi Sugam Accepted and validated. |

Re: Fibonacci Series- Counting and Recursion | |

Thank you sir I got it now. Must say this, good explanation. |

Re: Fibonacci Series- Counting and Recursion | |

Dear Sir, very useful article ,thank you. Is answer for fair toss question is 73 ,x+y=9+64? |

Re: Fibonacci Series- Counting and Recursion | |

Hi Sandeep Thanks for comment. Yes. Your answer is perfectly fine. |

Re: Fibonacci Series- Counting and Recursion | |

Hi Mohit Just try to see the pattern of the quantities in the two urns. Refer to a post above by Subhash Medhi. |

Re: Fibonacci Series- Counting and Recursion | |

BTW sir its mohil |

Re: Fibonacci Series- Counting and Recursion | |

I think Postman wala explanation is not correct...as we can hv many more cases...Believe that this question should be done by p&C instead of Fibonacci |

Re: Fibonacci Series- Counting and Recursion | |

Hi Durgadas I'd love to believe you. Please solve it. |

Re: Fibonacci Series- Counting and Recursion | |

thanx kamal sir and sorry for the mistake. |

Re: Fibonacci Series- Counting and Recursion | |

For Q5, will the recursion be of form: A(n) = A(n-1) + A(n-2) + 2*A(n-3) + 2*A(n-4) + 2*A(n-5) Is this right or are there other arrangements as well? |

Re: Fibonacci Series- Counting and Recursion | |

somebdy please post the solution steps for Mr. BLck, Mr red, mr orange derangement question!! |

Re: Fibonacci Series- Counting and Recursion | |

How 1-2 means if 1 is paired with 2, then other 4 persons (3, 4, 5, 6) can be paired in F(4) ways.Can u explain? |

Re: Fibonacci Series- Counting and Recursion | |

Hi Kamal, The answer to question on tossing of coin is 1535. Probability is 511/1024 as per my calculation. Please let me know if it is correct. |

Re: Fibonacci Series- Counting and Recursion | |

Hi Pratibha Please post the question also with your answer, so that it may be easy for everyone to respond quickly. |

Re: Fibonacci Series- Counting and Recursion | |

Hi Kamal Sir, Can you please explain derangement more with giving examples. It is confusing.I didn't get anything from above. Thanks. Regards, GM |

Re: Fibonacci Series- Counting and Recursion | |

thank u so much for this wonderful lesson sir, what will be the product of 1^1*2^2*3^3*…..*49^49? |

Re: Fibonacci Series- Counting and Recursion | |

hi sir,lovely article..... i have been reading your articles of late. it won't be wrong to say that i have fallen in love with what you do |

Re: Fibonacci Series- Counting and Recursion | |

Very good article. Another way to handle problems.. |