Posted tagged ‘time’

Daughters’ Ages

August 24, 2011

Two MIT math grads bump into each other at Fairway on the upper west side. They haven’t seen each other in over 20 years.

THE FIRST GRAD SAYS TO THE SECOND: “how have you been?”
SECOND: “great! i got married and i have three daughters now”
FIRST: “really? how old are they?”
SECOND: “well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”
FIRST: “right, ok.. oh wait.. hmm, i still don’t know”
SECOND: “oh sorry, the oldest one just started to play the piano”
FIRST: “wonderful! my oldest is the same age!”

problem: how old are the daughters?

Solution

solution: start with what you know. you know there are 3 daughters whose ages multiply to 72. let’s look at the possibilities…

AGES:            SUM OF AGES:
1 1 72            74
1 2 36            39
1 3 24            28
1 4 18            23
1 6 12            19
1 8 9             18
2 2 18            22
2 3 12            17
2 4 9             15
2 6 6             14
3 3 8             14
3 4 6             13

after looking at the building number the man still can’t figure out what their ages are (we’re assuming since he’s an MIT math grad, he can factor 72 and add up the sums), so the building number must be 14, since that is the only sum that has more than one possibility.

finally the man discovers that there is an oldest daughter. that rules out the “2 6 6” possibility since the two oldest would be twins. therefore, the daughters ages must be “3 3 8”.

(caveat: an astute reader pointed out that it IS possible for two siblings to have the same age but not be twins, for instance one is born in january, and the next is conceived right away and delivered in october. next october both siblings will be one year old. if a candidate points this out, extra credit points to him/her.)

this question is pretty neat, although there is certainly a bit of an ahafactor to it. the clues are given in such a way that you think you are missing information (the building number), but whats important isn’t the building number, but the fact that the first man thought that it was enough information, but actually wasn’t.

even if the candidate doesn’t know the solution, they could come up with some interesting thoughts. if they just stare at you and shrug “i dunno” then thank them for their time and don’t give them afogcreek pen.

Bumblebee

August 24, 2011

problem: two trains enter a tunnel 200 miles long (yeah, its a big tunnel) travelling at 100 mph at the same time from opposite directions. as soon as they enter the tunnel a supersonic bee flying at 1000 mph starts from one train and heads toward the other one. as soon as it reaches the other one it turns around and heads back toward the first, going back and forth between the trains until the trains collide in a fiery explosion in the middle of the tunnel (the bee survives). how far did the bee travel?

Solution

solution: this puzzle falls pretty high on my aha scale. my first inclination when i heard it was to think “ok, so i just need to sum up the distances that the bee travels…” but then you quickly realize that its a difficult (not impossible) summation which the interviewer could hardly expect you to answer (unless i guess if you are looking for a job as a quant). “there must be a trick” you say. eh, sort of i guess, enough to say that this question is a stupid interview question.

the tunnel is 200 miles long. the trains meet in the middle travelling at 100 mph, so it takes them an hour to reach the middle. the bee is travelling 1000 mph for an hour (since its flying the whole time the trains are racing toward one another) – so basically the bee goes 1000 miles.

there is no process to explain, so this question can’t possibly teach you anything about the person. they either know it or they don’t and if they already knew it before you asked, you’re not going to be able to tell when they give you the answer. so don’t ask this question. and if someone asks you this question, just tell them you’ve already heard it before.

100 Doors in a Row

August 24, 2011

Problem: you have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the 100th door.

question: what state are the doors in after the last pass? which are open which are closed?

Solution

For example, after the first pass every door is open. on the second pass you only visit the even doors (2,4,6,8…) so now the even doors are closed and the odd ones are opened. the third time through you will close door 3 (opened from the first pass), open door 6 (closed from the second pass), etc..

question: what state are the doors in after the last pass? which are open which are closed?

solution: you can figure out that for any given door, say door #42, you will visit it for every divisor it has. so 42 has 1 & 42, 2 & 21, 3 & 14, 6 & 7. so on pass 1 i will open the door, pass 2 i will close it, pass 3 open, pass 6 close, pass 7 open, pass 14 close, pass 21 open, pass 42 close. for every pair of divisors the door will just end up back in its initial state. so you might think that every door will end up closed? well what about door #9. 9 has the divisors 1 & 9, 3 & 3. but 3 is repeated because 9 is a perfect square, so you will only visit door #9, on pass 1, 3, and 9… leaving it open at the end. only perfect square doors will be open at the end.

Pilot to Mechanical engineer-the story so far.

August 23, 2011

“What do you want to become when you grow up, a doctor or an engineer?” asked my grandpa when I was a four year old. A question that evolved from a typical malayali mindset. Most of the mallu kids are taught to reply either doctor or engineer if somebody asks. My answer was pilot. A couple of trips to Trivandrum airport and my favorite toy aeroplane might have struck the spark in me. The ‘pilot bug’ gradually died down as it was replaced by police,inspired by some action movies.


I imitating a policeman ( Cops never aim & salute simultaneously :-P)

Quite ironically another movie which I saw when I was 7-8 years old, made me quit the desire to become a policeman. The movie was ‘Nanma niranjavan sreenivasan’ ( a Malayalam movie, Jayaram starrer). The hero of the movie was a police constable and in one particular incident the hero had to guard a deadbody, alone throughout a night. The next morning he was shivering with fever. That scene made an impact on my ‘weak heart’.

I fell in love with science @ school in 3rd or 4th standard. I dreamt of becoming a scientist . I stood odd in my class when teachers asked about ambition. The funniest part of ‘scientist story’ was that I did some experiments hoping serendipity.I still remember trying to burn various shrubs and grasses to discover biofuels when the hyped story of Ramar Pillai’s biopetrol was at its peak. Though I wanted to become a scientist, my mind wandered between astronomy, biology and geology.

I wrote the entrance exam for admission in Sainik school (9th std) and got shortlisted for the interview and medical checkup. To be frank I was more interested in the discipline , the sports and games and the huge campus, than becoming a defense personnel. The ‘scientist bug’ didn’t leave me. It was time for the interview and I had to strike a balance between ‘scientist’ and ‘defense personnel’. The interview panel consisted of three people, all of them defense staff. They shot the ‘ambition question’ and my answer was scientist in defense sector. They asked ” what do you mean ?” . I answered ” just like A.P.J Abdul Kalam”. Pokhran II and my interview happened in the same week and I went not stop about fission, fusion etc. They asked “what will you do if you don’t become a scientist?”. I replied ” I will join the defense services”. It didn’t convince them and finally I didn’t make it. They were interested in future soldiers, not scientists.

My grandpa’s question again came back when I finished 10th standard. This time from my parents. I changed my mind to engineer from scientist, but my parents wanted me to become a doctor( guess they were attracted by the social status and moreover my grandpa’s wish). I was in a reluctant mood , wrote the medical entrance and ended up in failure. After that I went for 1 year medical entrance coaching at a reputed coaching center . I neither gave 100% commitment to it nor dishearten my parents by saying a ‘no’ to the medical stream. I couldn’t get enough rank the second time also. The truth was that I often went in a ‘stealth mode’ practicing some maths problems which helped me fetch a fair rank in engineering entrance exam. Now there weren’t many options left other than joining bachelors degree course in engineering. I never blame my parents for the ‘lost’ 1 year, In fact I say I am responsible for the good or the bad that happen in my life.I should have taken a bold step. People (friends, relatives etc.) call it ‘lost’ year , but I never felt so and moreover learnt a couple of lessons in life.

Now it was time to choose the branch of engineering. The general trend was choosing electronics and communication . I was also in the mood until I got enlightened about Mechanical engineering by Dr. S. Jose , my relative and academic guru. Himself being a Mechanical engineer and Asst Professor, threw insight to the various aspects of mechanical engineering and I never thought twice to choose my stream. Mechanical engineering, being a ‘broad’ stream of engineering rendered me numerous options to choose- energy sector,oil and gas ,automobiles, aeronautical, aerospace,thermal.

I never had an interest in computer programming. I still remember, how tough the C++ programming was in 3rd semester for me, just managed to fetch a pass in that subject. 90% of the companies which came to my college for campus recruitment were IT companies. All the placement activities started in 7th semester. Though I wasn’t interested, just for the sake of attending tests and interviews, I participated in the drives. 3-4 companies came and I didn’t manage to get 1. Finally I got a job in a reputed IT company .I never wanted to join that company and told my intentions to parents. They advised it will be utter foolishness if I don’t join the IT firm, without having another job in hand. I was mentally preparing for a fight with them, thought of firing all guns to get a job in core field. I continued writing exams and attending interviews, and got a job in one of the fields which I dreamt of getting into- Oil & gas industry.My parents were happier than me. Thanks to all. Presently, striving hard to achieve my goals, and will be writing a part 2 to this post some years later. 🙂