A simple problem that led us to Ramanujan’s work on Integer Partitioning

September 12th, 2010 admin

Raghu, my cousin, sent me an email with the following problem a few months ago.

Question

Manish was on his way to an interview. On the way, he encountered his long lost cousin, Vijay, whom he hadn’t met in more than a decade. They started catching up on lost time. Manish learned that Vijay had 3 sons. When he asked about their ages, Vijay replied, “You’re going for an interview, right? Consider this a trial question. Figure out their ages from this: The product of the ages of my three sons is 36.” To this, Manish grumbled that he needed more information. Vijay, then, pointed to a sign board across the street that displayed the address of the area and said that the sum of the ages of his three children was equal to the last two digits of the pin code (zip code) of that area. Manish demanded still more information. Finally, Vijay said, “My eldest son wore a black shirt today. This is all I can tell you.”

What were the ages of the three children? Read the rest of this entry »

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Ammamma

September 1st, 2010 admin

“Ammamma…Boost…”, I would ask her for a hot malt beverage, as she would get busy in her tiny kitchen after her short afternoon nap on the hard concrete floor, with a strategically placed pillow for her head. Ammamma means maternal grandmother in my mother tongue, Telugu. Amma is mom, and ammamma is, literally, momom. She would then get busy preparing the late afternoon coffees for the elders, starting with the eldest – Tatagaru, and Boost for the kids. Although I mostly saw her only over summer holidays, this particular aspect of her routine was probably eternal. In fact, all her routines were seemingly eternal yet inexplicably fresh every time. She would hunker down at the old, grime-laden, two-burner gas stove sitting on the floor of her tiny kitchen and with what seemed like an impossibly tiny collection of utensils, groceries and gadgets, came up with the most exquisite of dishes. Simple fare it always was, and she was not a great cook, but the taste of her cooking was earthy and heavenly. Vegetables of all manner were shallow fried. Coffee and Boost was not served before being poured several times, alternating between two tumblers to generate froth (steamed milk). “Boost tagutawa, Kishtappa, aain?”, she would ask. The “aain?” was kind of like Amitabh Bachchan’s pan-laden mouth confirming something – “aain?”.

Read the rest of this entry »

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Out-of-the-box thinking

May 1st, 2010 admin

At the beginning of the previous post I had included a set of slides which propose the 4 squares problem and teach us that we should always be ready to think of a simple solution whenever possible. This theme caused a flurry of emails among some of my family members, and I would like to present some of the interesting ideas that arose in that discussion. Read the rest of this entry »

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The 4 squares problem – extended

May 1st, 2010 admin

A “4 Squares Puzzle” is doing the rounds over the internet nowadays. here are the original Microsoft Powerpoint slides which I received via email from my father. (Not sure who the original author of these slides is, but the slides report the author to be Nakit Yonetimi.) It may be useful to look over the pdf file once before proceeding. The question posted in the slides is different from the one I am going to pose, but going through the slides helps build context and helps get mentally warmed up.

The question I posed to myself after thinking through the puzzle was, “How can we divide a square into 7 equal parts with only a straight edge and a compass available?” Note that the question implies that we do not have a ruler or a scale. We have a straight edge, but without any markings on it to indicate inches or centimeters. Even if it did have the markings, such markings can only measure accurately up to a certain level. For example, say you have a scale with markings at the granularity of a millimeter. Say the square had a side equal to some irrational number, say or , or, even a simple integer which is not a multiple of 7, such as, 8 millimeters. There is no way to measure or or millimeters using such a scale.

There are at least 2 approaches to dividing this square into 7 parts. The first is a simpler approach and the second is slightly more involved. Let me talk about the second one first. The first one will then become easy to see. The main intuition behind the first idea is that a triangle’s area depends only on its base and height. If we can mark out 7 equidistant points along the square’s border, thus creating 7 equal bases, we can join the bases to the center of the square to create 7 regions with equal areas. The heights of these shapes will be equal, and the bases are equal by construction. Read the rest of this entry »

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The 3 Ds

September 17th, 2008 admin

My father’s maternal uncle, Dr. K. Ramamurthy, whom I call uncle also, responded to my email about “Games Indians Don’t Win” with some of his own words of wisdom, which I believe will be useful to many people; I reproduce them here with his permission. Read and think about it.

“During my management consultancy days, I’d start my classes with “Three Ds”: Discipline, Dedication, and Devotion.

We have to start anything in life, commencing with our earliest education, with the rigor of Discipline: regulated studies in terms of time allocation, understanding of what we study, practicing to become perfect, and humility not to be carried away by early successes (or depressed with early failures). You keep at it in spite of obstacles to reach the goal you set for yourself. Read the rest of this entry »

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We make it to India in 2008

September 12th, 2008 admin

Amidst the tussle between technology flattening the world and fuel prices beating it back to being rotund again – one making the world seem smaller and the other promptly stretching it back out – we planned a trip to India. Rising price of fuel had sent the ticket prices soaring, and at $1860 round-trip per head, the trip took on the shape of a mystical vacation, something to be enjoyed to the fullest – something to be planned to perfection while at the same time left open for surprises worth recounting. Traveling alone is usually a bland affair for me. Traveling with Kavita makes it a an order of magnitude more enjoyable. This time it was special also because this was Kavita’s first trip to India after our marriage three years ago. She was bound to enjoy and react to every little detail of the trip – shopping for tickets, the anticipation of meeting people back home, figuring out what all she wants to get from India, the actual flight and all its associated procedures, train travel, actually meeting people, taking in the changes since she last saw the country, and so on – and I was bound to enjoy her enjoyment. Of course, I had been to India only six months earlier, in December 2007. So this was mostly a trip for Kavita. Read the rest of this entry »

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Hello, Dr. Kavita Vadali!

September 19th, 2006 admin

August 2001 seems so recent. That was when Kavita came to the US to start working towards her PhD. After five years working on cell signaling pathways using the fruitfly as the model, Kavita successfully defended her work and was awarded a PhD in Biology by her advisors yesterday, Spetember 18th 2006. Though the convocation is in December and the magnitude of the achievement may be imparted a more visual facet then, I can appreciate what this day means to her and all the rest of us close to her.

Living in a tiny square patch of a town, in the middle of thousands of square miles of featureless flatlands, encouragingly named “Normal”, was expected to be hard for this single woman. She took to it like a duck to water. Having been on the phone with her almost every one of the days in these 5 years, I wouldn’t blame you if you thought that we were born with the cellphone on our ears, instead of the proverbial golden spoon in our mouths. I saw her develop lasting friendships. I saw her live an independent and brave life. I saw her work hard and cheerfully. I saw her build her life in her tiny, but beautiful apartment in Cardinal Court. Her friends, her teachers, her attitude and her spirit are all worthy of our thanks. She has done us all proud. She has given us hope and promise. Dedicated work, making the best of the opportunities you get, will get us rewards. Her mother, my mother-in-law, is to be especially congratulated. Her words, which usually carry a ring of innocence, humility and simplicity are in fact words of great wisdom. Her role in letting Kavita be herself, more than a direct hand in guiding her educational growth, is one important reason for Kavita’s achievement.

My role has been one of an honest and eager listener. Although I find very few understandable English words in her presentations or reports on her subject, I always tried to atleast keep myself aware of the basics of her field. Other than playing the joker to relieve both our stresses at the end of the day, my role has also been to positively appreciate the praise-worthy in her efforts, and critique the fallacies. I have always respected her work, her efficiency at it in her fruit-fly infested lab, her action-oriented approach towards a plan and the celerity with which she picked up something new. I have been always motivated by the positives in her. And this is a moment to reflect on these 5 years and to look towards the future as she puts the knowledge she has earned to good use. Congratulations, Dr. Vadali. You deserve it.

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Labor Day 2005 and the mini-reunion in Chicago

September 10th, 2005 admin

I would like to thank Kavita for typing up most of this journal from my handwritten and scanned notes, and my friend Praveen for motivating me to write about this trip.

Illinois is a place I visit often. Kavita and I look forward to meeting up on long weekends because they are a whole day longer than a regular weekend. The plan is always to meet up and spend time with each other. The way it ends up is we spend time with friends or family. And fortunately, both of us enjoy and work best in that mode.

For this September, the plans had been drawn over a long period of time – several hours spread over several weeks. That’s a big part of the fun; planning what we would do, once together. The plans, like I said earlier, always include meeting with friends and spending time with them, other than going some place nice and of course, some small doses of shopping.

The plans for this Labor Day, however, included an unusually enthusiastic attempt at meeting with many of my undergraduate schoolmates who studied with me at IIT Guwahati and now lived in or close to Illinois. The surprise was that I met up with all those friends I planned to meet, and more. Kavita, who enjoys being around people, loved every minute of it. And I loved it all the more. I was thrilled to see these wonderful people, and seeing Kavita’s delight doubled the effect. Read the rest of this entry »

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Crossword Clues

August 28th, 2005 admin

Kavita and I sometimes play this game over the phone, where I give Kavita a clue and she has to figure out the word. The clue is usually simpler than a cryptic clue in a crossword puzzle, bit I would still categorize it as a cryptic clue because there are two parts to the clue. Either both buttress the reason for the clue’s solution being what it is, or one provides the solution while the other part of the clue confirms it. In general I prefer cryptic clue crossword puzzles over easy clues, because with cryptic clues, each clue is a puzzle in its own right, and the crossword puzzle fills itself once you get the answer.

Syhamala and Srini also enjoy participating in this kind of a cryptic clue session. Lot of times, since the clues are created on the fly and are not “solidified” yet, they are twisted and mangled as the game proceeds leading to strange guesses and a hearty laugh. Shyamala suggested that I should atleast keep track of these, and therefore I am putting them together here.

Hereditary Clothing
Aim to shop at this store
Mated domesticated
Spherical dance
Direction I threw the stew in
India grows teas in this direction
Direction of old “you”s
Direction prickly things go
Mites multiplication factor
He levitated like this flower
Sue it’s for blowing your nose

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The Trip to India – Upanayanam and Marriage

March 12th, 2005 admin

This time the trip to India (left Raleigh on Jan 31st 2005 and returned on Feb 25th 2005), was hectic. It usually is, but this time was the big occasion. I was getting married. Kavita and I “tied the knot” on February 13th, 2005. The wedding was in Visakhapatnam. I met a lot of friends and relatives during this short trip. The days were filled with so much activity that the month just flew by. The trip started with a few days stay in Chennai, where I landed first in India. I stayed with my friend, Srinivasan Ramani’s parents. I had to get my US Visa renewed at the US Consulate in Chennai. It was great to meet Srini’s and Shyamala’s (Srini’s wife) families. I reached Vizag (as Visakhapatnam is called) on Feb 4th. Feb 10th was my Upanayanam (thread ceremony signifying the start of a young boy’s formal education). There were functions, pujas, lunches and dinners on a grand scale almost throughout the week. On 13th was the wedding, followed by my visit to Kavita’s place for a couple of days. Finally we were able to squeeze in a 3 day trip to the state of Orissa where we went to the tourist towns of Puri and Konark.

The pictures of this trip are here.

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