My Tryst With Autobiographical Number – The Story Of My First Interview

Today is a memorable day for me. Exactly 20 years ago, on 15th July 2000 I appeared for my first interview and successfully cracked it! So I thought of writing about it.

It was during the campus placements in the last year of Engineering. I had just entered the last year in year 2000. The campus placements season began on 9th of July 2000. The first company that came for recruitment was Wipro Infotech – a giant at that time! Oddly, their screening test consisted of Chemistry! I don’t know why. It was one of my weakest subjects in 12th. If my Mathematics was at 100, then the relative strength in Physics would be 75, in Biology it would be 60 and in Chemistry it would be 40. Hope you get the perspective.

So I was totally unprepared for questions related to Chemistry. After 12th I had not kept in touch with the subject and barely remembered it. As a result, I couldn’t qualify for the interview round of Wipro. That was my first experience of Campus Placements.

Then for next 4-5 days it was not known which was the next company visiting campus and when. Suddenly on 14th July we got to know that Infosys was going to come the next day.

To be honest, I had not even heard about Infosys till then. It sounds funny to me now, because I was so ignorant about the business world back then.

Infy wanted aggregate first class in all semesters and no backlog. I was eligible on that criteria. And decided to appear for the campus, without knowing much about the company.

When the Infy news broke, many of my classmates started congratulating me in advance saying that I would definitely get selected. On inquiring why they said that Infy selection pattern was all about puzzles and analytical skills/ logical reasoning.

I was known in my class for my love for mathematical puzzles. In the class, I would sit behind or in the corner and pass on some puzzles to next benches, which would eventually travel across the class and many would spend entire class solving them.

When most of the people in my class had only heard about Shakuntala Devi, and few had solved her puzzles, I was well into likes of Martin Gardner, Sam Loyd, Dmitri Fomin et al. I had very good collection of diverse mathematical puzzles, riddles, brain teasers and logical/analytical reasoning questions which I had collected over 10 years before that. It was my hobby and passion.

So naturally when the selection process itself entirely consisted of solving puzzles, I was on my home turf. And hence many thought I would get selected.

After hearing that I was not necessarily confident that I would get selected; that was hardly on my mind. I was rather excited to solve some puzzles and hence was looking forward to the selection process.

I vividly remember the selection process on 15th July 2000 – exactly 20 years ago. It was a Saturday. I went to my college at around 9 AM with a handwritten CV. I didn’t have computer at home in those days. I had already submitted one copy of CV during Wipro interview and didn’t have any spare one. Also, in those days internet cafe and printers were not so ubiquitous. Most importantly, I simply didn’t feel it mandatory to take the effort to run around and print CV on 14th. Being proud of my decent handwriting, I rather chose to write it by hand – an opportunity to impress the interviewer. I remember using black, blue and green ink pens to highlight and underline keywords.

Interestingly, I didn’t even wear shoes. I didn’t have leather shoes in college. Only sports shoes, which didn’t go well with the formal trousers and shirt. So I wore chappals – yes, not even sandals. Plain chappals. Now I when I think about it I feel appalled by my casual approach. But at that time I didn’t understand the gravity of the whole campus interview process or corporate culture. I was simply not oriented for positioning myself as a prospective employee in a large and hugely reputed organisation. I was still an ignorant student happy in the academic world.

Anyways, so I reached college (in formal clothes and chappals) at 9 AM and went through the initial formality of submitting photocopies of mark-sheets, (handwritten) CV and other details. Then we were asked to write an aptitude test consisting of logical reasoning/analytical questions. I think it was for 1 hour and had some 10-12 puzzles. Some were objective (you had to solve puzzle and choose an alternative) and few were descriptive where you had to solve the puzzle step by step. It didn’t have any General Knowledge questions or (thankfully) Chemistry questions.

That went pretty smooth. I solved all of the questions and I think I must have got most of them right. So I was shortlisted for the interview round. Some 400 students across all faculties (I was from Mechanical Engg, but the others were from Computer Science, E&TC, Instrumentation, Civil, Production, Industrial Engg etc) from 3 Engineering colleges had appeared for written test and 100-odd got shortlisted for personal interview.

There was a short recess after the written test and the shortlisted candidates were assembled for the personal interview round and made to fill a long, almost exhaustive form. At that time I felt like it was something really important. Infosys processes were amazing and meticulous. There were 5-6 volunteers (Infy employees) helping us with any doubts and there were 2-3 HR people and 2-3 senior grumpy looking folks. Then everybody was divided into 3 groups as there were 3 interview panels. I was assigned to Panel 2. Interesting coincidence, I thought! Sum of the digits of my birthday adds up to 2. My hall ticket number in 10th and 12th class (which were important exams till then) added up to 2. My scooter (Bajaj M-80) had a number plate which added up to 2. My roll number was 2. Infosys was the second company visiting campus. And now I was assigned to interview Panel 2. And every panel had 2 people. So much for coincidence.

I have this habit of exploring and conjuring up patterns and connections. It doesn’t to anything significant, but it keeps my mind busy, my brain active and it kills time.

All this was going on in my mind while we were waiting for the interviews to start. The HR had told us that the personal interview process would be simple. A panel of 2 people would ask us questions related to our aptitude test, give few more puzzles to solve, and have a general chat based on our CVs (just to ensure that we were adequate at leisurely conversations, and articulating our thoughts). I was elated because I would get more puzzles!

Once the interviews started, I was the first one in my panel – don’t know if it was because I had done well in written aptitude test or because my surname started with “A”. In Panel 1, the first person scheduled for interview looked very tense. I don’t know if he was from my college (some other branch) or a different college, but he was not ready for interview. So he requested the HR for some more time and the next guy was sent in. HR asked me the same and I said I was ready. It was not confidence, but just the thought of getting done with this process, rather than waiting in anxiety. So I went in to Panel 2.

The panel consisted of 2 people – one was the senior grumpy looking guy and the other was one of the volunteers. After initial meet and greet, the grumpy looking guy (let’s call him GLG) was looking at my handwritten CV and the volunteer guy (let’s call him VG) was looking at the form I had filled. The GLG murmured something about my handwriting and said if I had heard of MS Word. It was probably a sarcastic comment, but I took it literally and said that I was conversant with MS Word 98 but didn’t have computer at home. Then the VG read about my hobbies and said: “So you play chess?!” I nodded. I felt VG was not sarcastic or probing, he genuinely wanted to know. Probably he was a player too.

Then both of them looked at my answer sheet of aptitude test and said, let’s start. So VG put a couple of blank pages and pencil in front of me and said “We’ll give you three puzzles. You’ll have 3 minutes for each. We’ll inform you after every minute to help you manage time. And then we’ll wind up with a couple of questions. OK?” I nodded.

VG gave the first problem.

There are 100 closed doors numbered 1 through 100, all are initially closed. A person walks past each door and toggles the state of the doors which are multiple of 1 (i.e. all 100 doors). Toggles means changes the state (Open, if the door is closed, and Close if the door is open). And then second person walks and does the same. And so on until 100. Finally, which door numbers are closed and which are open.

I had solved the problem earlier. It was a typical problem for algorithms – usually for C/C++ beginners. However I had solved it without using algorithm. I took my time to give appearance that I was solving it for the first time. So shortly after 2 mins, I said that I had solved it and they asked me to explain.

“Any number can be expressed as multiplication of a and b. So if “a”th person is going to toggle a door, “b”th person is going to toggle it back – so that the original state of the door is maintained. For example, take door number 18. 18 can be written as “1×18” and “2×9” and “3×6”. So if “1” is going to open the door, “18” is going to close it. If “2” opens it, then “9” closes it again. And if “3” opens it, then “6” closes it. In nutshell, the door remain CLOSED (it’s original state). This is true for every door, EXCEPT square numbered doors – because in those cases “a” and “b” are same. So it’s not “axb” but “axa” i.e. “a square”.

So the answer was: “All square numbered doors would remain open.”

VG looked impressed with my logic. GLG looked happy and asked me if I used to solve Shakuntala Devi puzzles. I told him about Martin Gardner too and now he seemed impressed.

So he gave the next puzzle.

“There is a number which ends with digit “2” such that if you move this last digit in the beginning, the new number thus formed is twice that of the original. What is that number?”

I wrote 12 and realized that if I move 2 in the beginning it give 21, and not 24 (which is double of 12). So 12 was not the answer. Then GLG asked me if I had understood the problem and wanted to clarification. I said: “No…the number seems to be a large one. You haven’t specified how many digits”. GLG smiled; he knew that I had understood the problem.

So I started scribbling. If the last digit was 2, the one before it had to be 4, and the one before that 8, and the one before would be 6 (with carry 1), and the one before would be 3 (2×6 plus carry 1) and so on. So where do I stop? Till the cycle starts repeating itself. I kept going on and on, carefully checking the digits intermittently. Because, I had solved the puzzle…it was just executing the sequence and getting the answer and I didn’t want to goof up in that. Finally the sequence repeated. The number turned out to be 18 digit long!

The answer was: “105263157894736842”

I explained the logic to the interviewers and both seemed happy. Then GLG said, “Let me try a different one for the last puzzle. My favorite”. So he took out a piece of paper from his pocket and read the last puzzle.

“21200 is a peculiar number. If you write the digits places from left to right starting from 0 on top of the number, you get an interesting observation.

0 1 2 3 4

2 1 2 0 0

So the first digit “2” indicates how many ZEROs there are in this number. There are 2 zeroes.

Second digit “1” shows how many ONEs (the place of that digit which is shown on top) there are in this number. There is only 1 ONE.

Third digit “2” indicates how many TWOs there are in this number. There are 2 TWOs.

Fourth digit “0” indicates how many THREEs there are in this number. There are 0 THREEs.

Fifth digit “0” indicates how many FOURs there are in this number. There are 0 FOURs.

You have to identify an eight digit number satisfying this property (so the position digits would go from 1 to 7).”

Well, the puzzle was overwhelming! It took a few seconds to grasp all the information. GLG asked if I had understood the puzzle and I said yes. He asked: “So can you solve?” I said: “Let me try”.

I wrote 0 through 7 numbers at the top in bold and big size. Those were going to be permanent. I had to try different digits below that…which would satisfy the said property. I immediately realized that the number could not have digits 8 and 9, because the header numbers were from 0 to 7 only. I started scribbling different combinations.

“1 minute over” GLG warned me. I continued. “2 minutes over” GLG said. At that time VG stepped to inform the next guy to be ready and returned back. Soon GLG announced that 3 minutes were over. I had not finished the problem.

GLG asked me to explain what I was upto. After listening to me he asked “Can you solve it if I give you one more minute?” I had not clue, but I had liked the puzzle. It was interesting and I wanted to continue! So I said, “I’ll try”. So GLG said, “Continue for another minute”.

I did. And luckily enough, I solved it within the next minute. Probably GLG had figured out from my approach that I was on right path and close to the answer.

The answer was: “42101000”.

It’s the eight digit number satisfying the said properties.

GLG was impressed and asked me if I could codify it. i.e. if I could write an algorithm for the iterative process I had done. I said I couldn’t. I just started with all “0”s and used iterative process to adjust different digits. He said: “Then try it. Try to develop a generic algorithm. Also find if there are other 3-4-6-7 digit numbers which satisfy this condition”.

I was very happy! He had given me more puzzles to solve at home 🙂

With that my interview came to and end. Well, not really before we had another small round of sharp witted exchange. VG asked me if my favorite player was Kasparov or Anand. I said Anand is role model, but I like Kasparov more as a Chess player. Then GLG chipped in and asked, “You said you have studied Chess. Do you know Sicilian?” I looked at him and something inside me told me that he was bluffing. He himself didn’t know what Sicilian Defense was. He had probably just heard the word Sicilian and was trying to test me.

So I too decided to be combative! It was instant, impromptu thinking, not a well thought one – just instinctive. I decided to expose his facade and asked him “Which variation in Sicilian? Dragon or Najdorf?”

GLG knew that I knew that he didn’t know Sicilian and was just posturing. And that I had cleverly turned around the question rather than answering him. My counter-question was both – an answer to his question and a wise crack at exposing his facade. He knew it and smiled. VG too understood and he smiled too. And I…well, I am always poker faced…so I didn’t smile. But the feeling was the same.

I knew I had done well in the interview! I was satisfied. I was not worried if that was good enough to get me selected. So with final good wishes, I walked out and went back to the main hall.

I was very relaxed. It was not a feeling of achievement, but one of being content, at peace. I was OK with whatever would be the outcome of interview.

Since I was the first person in my panel and there were ~30-35 in each panel, the whole process (which started at noon, after the aptitude test in the morning) moved really slow. We waited the whole day and the final results were announced at 8 PM or so. And to me joy (but not surprise), I was selected!

It’s been 20 years today since that campus interview took place and it has been my most enjoyable interview ever…because it was just puzzles and more puzzles!

Post Scriptum:

I later discovered that the “21200” puzzle was about “autobiographical numbers“. And do you know something really interesting?

2020 is an autobiographical number!

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