Wednesday, June 20, 2018

# Problematics: The breeding habits of Facebook shares and Fibonacci rabbits

## The bunnies have a gestation period, however short, but the shares can multiply 24×7.

The Fibonacci sequence. At the age of two months, rabbits have their first twins, followed by a new pair of twins every month. (Source: Express illustration by Kabir Firaque)

What multiplies faster, proliferating rabbits or Facebook shares? The bunnies haven’t a chance, even if they breed at the rate assumed by Italian mathematician Fibonacci.

Take a young Mr & Mrs Rabbit, Fibonacci said, and assume that at the age of two months they have their first babies, another male-female pair. From then on, the parents have a new pair of babies every month, always a male-female couple. All these new rabbits follow the same routine, starting with twin babies after two months and continuing every month. If you extend my colour-coded illustration to infinity, the total number of couples month by month will be: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…

This is what people call a Fibonacci sequence. Note that every term is the sum of the previous two. Note also that 1 and 144 are perfect squares.

Puzzle#15A: When will the sequence throw up its next perfect square, if at all?

Unlike the rabbits, one Facebook share can breed new shares 24×7. Facebook, however, can be a double-edged sword. It has wonderful users who shared around last week’s puzzles to an extent unprecedented so far. But a handful of them undid some of that help by posting the answers on Facebook itself.

In a free Internet, no one can stop them if they want to spoil other people’s fun. Regular readers, however, continued to have fun by following the Standard Operating Procedures, which means they sent their answers by email.

Puzzle#14A(i) is basically adding up to 2015 twice. The age a person will reach this year when added with his/her birth year will give us 2015. Also, years in office when added to the year each leader assumed office will give us 2015 again.

Anirudha Hulsurkar (Student, IIT Roorkee)
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Dear Kabir, the solution to Puzzle#14A(ii) is as shown in the image. The previous positions of the matchsticks are indicated by a thin black line.
Jaysun Antony Alumkal (Coordinator, Academic Committee, IIM Raipur)

Puzzle#15B: The day a post comes up on Facebook, 10 people share it. Each share is read by 100 new people, 10 of whom share it again the following day. Each of those shares, again, is read by 100 new people… and so on. Assuming everyone logs on at some point or the other, how many days will it take for the shares to reach all of Facebook’s 1.44 billion users?

My request stands, answers by email rather than on Facebook, although I know some people will simply not listen. Meanwhile, you 4.2k kindly folks who “liked” my blog last week and shared it 1,307 times, can you continue the promotion, please? Deeply grateful for your voluntary help.

What you wrote

Two of last week’s five easy puzzles dealt with, here are the answers to the remaining three.

Thank you for this great set of puzzles. In Puzzle#14A(iii), take elements B, C, N, O and Ar. The letters can be rearranged to form CARBON.

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In #14A(iv), both glasses weigh the same. For floating objects, weight of displaced water = weight of object. So weight of second glass = weight of water in first glass – weight of displaced water + weight of wood = weight of water in first glass.
Biren Parmar (PhD student, Texas A&M University)
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For #14 B, the answer is Audrey Hepburn. The Hollywood movie was ‘Gigi’, half-French actress Leslie Caron. The 1960s film Audrey Hepburn did which swept Oscars: ‘My Fair Lady’. Best Actress in 1964 was Julie Andrews for ‘Mary Poppins’. Though all the problems were relatively simple, I liked them, especially the actress one. Regards,
Bindia George (Kochi)

Solved all five puzzles: Vivek Jalan (Customate Systems; Mahalaxmi Seamless Ltd), Sathya Prakash (New Jersey), Sampath Kumar V (IIM Kozhikode alumnus), Anindita Basu, Biren Parmar, Bindia George

Solved four out of five: Nitin Saraswat (Bank of America, Gurgaon), Anirudha Hulsurkar, Jaysun Antony Alumkal