Tuesday, April 16, 2013

Interesting Numbers...



Problem 1:

1. Take any three-digit number where the first and last digits differ by 2 or more.
2. Reverse the digits, and subtract the smaller from the larger one.
3. Reverse the digits again
4. Add to result in 3 to result in 2

Solution: Always you will get the number “1089"


Problem 2:

1.Take a four digit number with all different digits
2.Sort the digits in descending order and call it A
3.Sort the digits in ascending order and call it B
4.Calculate A-B
5.Repeat the process and get the unique number

Solution: After few iterations u will get the magic number "6174"


Problem 3:

Take a number (call it NumberOne) and sum up all its factors. Call it NumberTwo. Sum up all the factors of NumberTwo. If it is equal to NumberOne then these two numbers are called amicable numbers. For ex: 220,284
Sum of factors of 220: 1+2+4+5+10+11+20+22+44+55+110 = 284
Sum of factors of 284: 1+2+4+71+142 = 220
Find out these kind of amicable pairs.

Solution:  http://oeis.org/A063990

Problem 4:

If the sum of the factors of a number is equal to that number then it is called a perfect number …for example 6 Is a perfect number because factors of 6 are 3, 2, 1 and 3+2+1 = 6. 28 is a perfect number because factors of 28 are 14, 7, 4, 2, 1 and 14+7+4+2+1 = 28.Find out the magic numbers less than 100000 ( FYI there is only one magic number between 100-1000 and only one magic number between 1000 – 10000 and no magic numbers between 10000-100000).

Some interesting facts:

1. If 2exp(n)-1 is prime, then 2exp(n-1)*(2exp(n)-1) is a perfect number
2. All perfect numbers are even and in the form 2exp(n-1)*(2exp(n)-1).
3. There are no odd perfect numbers. If you find one file a patent
4. Any odd perfect number must exceed 10exp(300) and must be divisible by a prime power exceeding 10exp(20)
5. Perfect numbers are infinite. If you can prove the finiteness file a patent

Solution: http://oeis.org/A000396

Problem 5:

Take a number (call it NumberOne) and reverse all its digits. Call it NumberTwo. If NumberTwo is divisible by NumberOne then they are reverse digit divisible numbers.
For ex: 721 reverse: 127. 721 is divisible by 127.
Find out this kind of unique numbers.

Solution: Please ping me at: Gopala.Krishna@outlook.com

Problem 6:

There are two persons A and B
A knows the product of two numbers
B know the sum of the same two numbers
The numbers are between 2- 99
They started talking to each other
4 sentences exchanged between them
Based on the conversation we need to find the numbers

The conversation is:
1st: A says to B that he don't know the two numbers
2nd: B replies that i know u don't know the two numbers
3rd: A then replies NOW i know the two numbers
4th: B then replies NOW I ALSO know the two numbers

Solution: Please ping me at: Gopala.Krishna@outlook.com

Problem 7:

If a number is a square of an integer, and also the difference between cubes of two consecutive integers, then the square root of this number can be expressed as a sum of squares of two consecutive integers. For e.g. 169 = 512 - 343, so 13 = 4 + 9.
Find this kind of unique numbers.

Solution:  Please ping me at: Gopala.Krishna@outlook.com

If you like to know some more interesting problems of this kind please visit http://oeis.org/ or ping me at: Gopala.Krishna@outlook.com

Saturday, October 27, 2012

The Story of Mr.Subtle "A True Mathematician"


Mr.Subtle failed in mathematics. He always wondered y mathematics is so boring and y mathematics teachers are so cruel. Mr. Subtle always suffered from questioning attitude and especially on mathematics. One day Mr.Subtle’s mathematics teacher Mr.Pasha said : In the equation x+3 = 5 if 3 is moved to the right side of equals it becomes -3 (x= 5-3). Mr.Subtle really wondered how this magic is happening till the time he got to know from Mr.Pasha that he is simply adding -3 on both sides of equals to make this magic possible.
Mr.Sublte always had fun teasing mathematics teachers and Mr.Pasha is his first victim. One fine day Mr.Pasha asks Mr.Subtle’s close friend that how many zeroes are there in a million.Indians were only taught about crores and lakhs unlike americans so Mr.Subtle’s friend is really confused. Mr.Subtle also donno the exact answer but he thought of teasing Mr.Pasha and so raised his hand.
Mr.Pasha: Hey Mr.Subtle…do you know the answer for this question?
Mr.Subtle: Yes sir…but before answering this I have a question for you…
Mr.Pasha: What’s that?
Mr.Subtle: In which numeric system? Binary? Decimal? Hexadecimal?
Mr.Pasha: I got your point. Let’s assume decimal system.
Mr.Subtle: Then are you asking about zero’s to the left side of 1 or right side of 1?
Mr.Pasha: Does that really matter?
Mr.Subtle: Yes…if the zeros are on the left side of 1 we can put as many zero’s as we want so a million can have infinite number of zeros on the left side of 1.
Mr.Subtle felt good for saving his from from Mr.Pasha.
Another fine day Mr.Pasha was teaching about complex numbers and was explaining that i = Squareroot of -1 and i is the core foundation of complex number system. Mr.Subtle really got confused and asked Mr.Pasha that y he is only interested in sqrt(-1) and not cuberoot of (-1) or 4th root of -1 and so on.Now Mr. Pasha is confused.
Then onwards Mr.Pasha got little bit uneasy for all Mr.Subtles hand raising “I know the answer” questions. From the core of his heart he felt like he has to take revenge on Mr.Subtle some day.
Finally, that day has come. Mr.Pasha was explaining about the limits in calculus and how limits becomes the foundation of differential calculus. Mr.Subtle raises his hand.
Mr.Subtle: if the value of 0/0 is not defined then y u are trying to make sense of it by introducing limits?
This time Mr.Pasha got a chance to tease Mr.Subtle. He never wanted to let it go. Though he donno the exact answer for Mr.Subtle’s question he wanted to answer his question with another question.
Mr Pasha: The answer for your question is here…suppose you and your girlfriend are separated by a distance of 100 meters and to reach your girlfriend….. in every one hour you travel a distance of half of the distance needs to be covered (I mean in first hours you can cover 100/2 50 m and in second hour 50+50/2 means 75 and in third hours 50+50/2+50/4 means 87.5 mts and so on…). In how many hours you can reach your girlfriend?
Mr. Subtle then got to know that he can’t reach his girlfriend by solving Mr. Pasha’s problem and really appreciated why limits exists and the way Mr. Pasha explained the limits concept. But he really wondered whether we can apply this limits concepts to zero power zero.
Another fine day Mr.Subtle got a doubt that y Mr.Physics teacher taught him up to acceleration and what happens if we differentiate acceleration wrt to time (s is displacement ds/dt is velocity and ds square/dt square is acceleration  and what if we differentiate one more time I mean what is ds cube/dt cube)
Since Mr.Subtle is more comfortable in teasing Mr.Pasha he posed the same question to Mr.Pasha. Fortunately Mr.Pasha has a partial answer. “If we differentiate acceleration u will get a Jerk!!! If you want to differentiate more and get to know the answers for the same go and join a school called IIT in India. Mr. Subtle felt bad that Mr.Pasha might be calling him jerk but he took the latter advice very seriously.
In the first year of engineering Mr.Subtle was introduced to computers and he was told that computer can answer any damn question in the world. To his surprise he found it’s mostly true when he typed something on Google and when he learnt about artificial intelligence.
One day out of curiosity Mr.Subtle asked the professor “Sir tell me at least one interesting thing which computer brain can’t do and only human brain can do?” ….professor immediately replied “Computers brain can’t pose questions like you…especially context sensitive questions”.  
Because of ethical hacking addiction Mr. Subtle cultivated a never give up attitude.  His virtual roommate Mr. VK Reddy once got pissed off with his never give up attitude and thought let’s tease Mr.Subtle with a Subtle Question. He handed over an indefinite integral to Mr.Subtle and said if you are a true mathematician solve this question in 24 hours. Our “never give up” Mr.Subtle sacrificed  his sleep, girlfriend fun, chatting, eating,  phone calls  and even  hacking fun to solve this damn indefinite integral. Mr. Subtle know that Mr VK Reddy is a kind of a guy who knows only one way of shutting down a computer i.e. switching off the power button on the switch board.  Mr. Subtle wanted to prove that he is a true mathematician to Mr.VK Reddy. 24 hrs passed on. One day passed on…One week passed on….Mr.VK Reddy collected all the papers which Mr.Subte is wasting on daily basis and started earning money by selling them to waste paper wala…one month passed on…one fine day Mr.VK Reddy decides his earning on waste paper business is more than enoug and conveys to Mr.Suble that “Not all indefinite integrals have solutions and in the same way not all life problems have solutions and never give up attitude should always have limits”…hmm then hearing about limits Mr.Subtle got to remember Mr.Pasha  and got to know y  Mr. Pasha  gave that last advise. Mr.Subtle found a true mathematician.
Then onwards Mr.Subtle always tried impressing Mr.VK Reddy  by discussing some of his unusual mathematical findings like the number between two consecutive primes is always divisible by 6 ( 17,19 …18 is divisibe by 6 ..41, 43 …42 is divisibe by 6) no magic numbers exists in 6 digits (magic number is: sum of factors of a number should be equal to the number for ex: 6 = 2+3+1 and 18 etc..) but Mr. Subtle never lived upto the expectations of Mr. VK Reddy.
Mr.Subtle never expected that more surprises are waiting for him in corporations….Read on……

Monday, September 13, 2010

Some interesting puzzles


Let me introduce you some interesting puzzles.


During my intermediate days, one of my physics lecturers asked me this puzzle.

Puzzle 1:
A Bear falls from a mountain of 500m high and dies on the spot. The time of fall is 10 seconds. Using this information find out the color of the bear…I mean the “hair” color of the bear. (You might be wondered what is the link between the above information and the hair color of the bear..But there is a link..Find it out!!!)

This is another interesting puzzle which I have c’n on the T-Shirts of IITian’s at IIT Mumbai. If u is a true Computer geek you can definitely interpret the meaning of this sentence.

Puzzle 2:
There are 10 types of people …those who can interpret binary and those who cannot.


Please ping me at gopala.krishna@outlook.com for the answers for the above puzzles

Saturday, February 20, 2010

Rhythm based Search Engine Framework

From last few days a rhythmic tune has been running over my mind 24/7. I googled over the internet for the songs, background scores and ended up listening\downloading so many songs, but couldn’t be able to find the song which embeds this tune. Though I know the exact tune (the programmatic rhythm) I couldn’t be able to search over the internet based on the tune or rhythm.
After putting efforts for around 20-30 days I finally figured out the song using Google search. As I guessed it’s scored by none other than the music legend Ilayaraja. I used to hear this tune during my school days and at that time I don’t even know abcd’s of music …but it seems I enjoyed this tune a lot. That’s the power of melodious music.
Then suddenly an idea flashed in to my mind…y can’t we develop a search engine which could be able to search the rhythmic tunes embedded in songs \background scores?
For example, I have a simple tune like “Ta na na na naaaaa na……….. Ta na na na” ( This tune is from “Chariots of fire” as u might have guessed) it would be better if we have a search engine which grabs all the songs, background scores which embeds\”is based on” this tune.

Some of the basic functionalities which we can expect from this Search Engine Framework:
1) It could be able to search all musical compositions based on raga
Let’s call it as “Raga based search”
Example: All background scores\songs which embed Madhuvanti ragam
Also, it would be better if we have a provision to add filters like: Only Illayaraja’s or
Balamurali Krishna’s works in Madhuvanti raga
2) It could be able search all musical compositions based on a fugue
Let’s call it as “Fugue based search”
Example: All fugues scored in C minor
Filter: J.S. Bach’s, Mozart’s fugue works
3) It could be able to search all musical compositions based on arbitrary rhythmic strings
Let’s call it as “Rhythmic string search”
Example: String like “Ta na na naaa na”, “ Taaa na na nananaa….Taa na na nanana”
4) It could be able to search all extended musical compositions like Symphonies
Let’s call it as “Symphony based search”
Example: All Choral symphonies or All Pastoral symphonies
Filter: Ilayaraja’s and Beethoven’s symphonies

At this point of time I could be able to figure out these four basic functionalities in this search framework and you can look out for more additions in my next blog posts.
As you might have guessed, right now I am working on basic technology needs (voice recognition, rhythm capture, Harmonic progression capture, musical notation parser etc) for developing this product. If you have any suggestions or if you know any existing product with this kind of functionalities please let me know.

References:
http://webspace.webring.com/people/dv/vasudevanvrv/carnatic/raagams.htm
http://www.oocities.com/ilaiyaragam/index.html
http://www.jsbach.org/
http://en.wikipedia.org/wiki/Ilaiyaraaja
http://www.its.caltech.edu/~tan/Mozartreq/main.html
http://en.wikipedia.org/wiki/Beethoven

Monday, October 6, 2008

Expressiveness + Movies + Love + Work + Mind

Instead of getting buried inside the search framework stuff all the time, thought of writing an article on Expressiveness + Movies + Love + Work + Mind etc …

Recently I heard an interesting quote from one of my friend at Microsoft – “Most of the people in this world are not much expressive just bcoz they fear that something may go wrong if they express what they believe in”. And most of them don’t really want to bear the consequences if something goes wrong. Yes he is right.

Movies and expressiveness – There is tight coupling between movies and “expressiveness”. I haven’t seen a single person who doesn’t like movies. Why? Because most of the things which we can’t do or express (what we really want to do) in real life can be expressed through movies/tales (But we seldom get a chance, unless we r a director or novelist...). I have seen people complaining that most of the movies made nowadays are related to Love (90%). Why? Just bcoz most people seldom like to express love in the real world (I am not inferring only the teenage love). Hence this topic becomes an integral part of movies and tales. Personally, I feel like Love is something which needs to be expressed. Whatever we don’t (or can’t) express in real life that things become an integral part of movies/tales (and of course our dreams too…).

Love – Let me ignore all the other flavors of love (Mother – Son etc) and just focus on love which happens with a boy and gal at an age of 18-28. I have seen many ppl (especially teenagers) who are ready to do anything for love. But teenage love is dangerous just bcoz at that age we can’t make distinction between real “Love” and an “Infatuation” (of course some people do...But definitely not at the age below 19). There is quotation like “Everything is fair in love and war”… yes that’s really true but applicable only for love and not for Infatuations. So one needs to know the clear distinction between love and infatuation whenever they talk about (or implement) the rules of love. I am sure every person in this world goes through a series of infatuations (even though they may not experience love...i.e. teenage love) in his life time. Personally I feel like we shud enjoy them and shouldn’t take them seriously as long as they doesn’t harm anyone. Love is more enjoyable than an infatuation.

Let me quote some good dialogues from my favorite movies. They really make u know the power of love. To demonstrate the power of love I am using movie dialogues instead of real life scenarios just bcoz as explained above what we can’t express in real life can be better expressed through movies\tales.

Movie: “A Walk to Remember”
Shane west: r u scared of death?
Mandy Moore: I am scared of not being with u.

Movie: “Jab We Met”
Kareena Kapoor: Am I doing the right thing (At the time of eloping)
Shahid: No, You are not doing the right thing. But it’s ok...u only said that everything is fair in love…

Movie: “If Only”
Paul Nicholls: In your life, if u has one day left what would you do
Jennifer Love: That's a hard question.
Paul Nicholls: I just like to know
Jennifer Love: Well, Shoe shopping....eating.....
Hmm...It’s an easy answer..I will spend up with u...just being together..like
now ..doing nothing...

Mind and Heart – Whatever we express, originates from mind, heart or Mind + Heart. When we are in love, generally we use only our heart (heart goes to 100% utilization level at that time). But at that time, we have to use our mind too up to some level... The obvious question is “why?” …”In order to figure out whether it’s really love or an infatuation”. If it’s really love, go ahead and enjoy using your heart at 100% utilization level.

The most important part – WORK and LEARNING - Mind and Heart plays an important role in Working\Learning. People who use only mind during work\learning can’t make better products unless they put their heart into what they do. Most successful people in this world are the ones who put their hearts while doing work...I mean they like and love what they do from the core of their heart. So while working or learning anything… love the work and keep right blend of heart and mind into it. By putting your mind, u will get the creative output and putting ur heart u will get the real satisfaction i.e the real things which we expect while doing work or learning something. Finally, what I mean to say is put a correct blend of Mind+Heart while working or learning something. That fetches u the creative output and outmost satisfaction.

Disclaimer: The above inferences are from my real world experiences and sometimes these fundaes may look like bullshit if we look them from a different angle

Wednesday, September 3, 2008

Truth of life

God created the Donkey. And said to him.'You will be a donkey. You will work un-tiringly from sunrise to sunset carrying burdens on your back. You will eat grass, you will have no intelligence and you will live 50 years.
'The donkey answered :'I will be a donkey, but to live 50 years is much. Give me only 20 years'
God granted his wish.
God created the Dog. And said to him :'You will guard the house of man. You will be his best Friend. You will eat the scraps that he gives you and you will live 30 years. You will be a dog.
'The dog answered:Sir, to live 30 years is too much, give me only 15 years.
God granted his wish.
God created the Monkey. And said to him :'You will be a monkey. You will swing from branch to branch doing tricks. You will be amusing and you will live 20 years.
'The monkey answered :'To live 20 years is too much, give me only 10 years.
'God granted his wish.
Finally God created Man... And said to him :'You will be man, the only rational creature on the face of the earth. You will use your intelligence to become master over all the animals. You will dominate the world and you will live 20 years.'Man responded :'Sir, I will be a man but to live only 20 years is very little, give me the 30 years that the donkey refused, the 15 years that the dog did not want and the 10 years the monkey refused.
God granted man's wish.
And since then, man lives 20 years as a man, marries and spends 30 years like a donkey, working and carrying all the burdens on his back. Then when his children are grown, he lives 15 years like a dog taking care of the house and eating whatever is given to him, so that when he is old, he can retire and live 10 years like a monkey, going from house to house and from one son ordaughter to another doing tricks to amuse his grandchildren.

Friday, March 21, 2008

Article on IITians attitude...

This was originally posted at
http://helloji.wordpress.com/2008/03/05/iit-insufferable-indian-tribe/
The post is really hilarious and bit unreasonalble frm IITian’s point of view. if u look at any organization i am sure we can find fair number of IITian’s in the top management which proves that they are really capable.. take any reputed company (like microsoft) u can find fair number of IITian’s. Some of the core qualities IITian’s have ( which u can’t find in non-IITian’s) :
Never give up attitude
Excellent problem solving skills
Structured way of thinking
Ability to learn things very fast
Love to do challeging work
Also, i don’t agree with the argument that IITian’s always boost or market IIT brandname …infact they are not the persons who popularized the IIT brand name..non-iitians are the ones who actually popularized it realising that it’s worth to be popularized. The reason behind this popularity — IITians outperformace in almost every field.Being an IITian i never used IIT brandname in any of my initial conversation. i was made to use it just because after talking for a while ppl used to ask me “what’s ur background??”. This type of situation happens to most of the iitians bcoz the way of thinking of iitians is completly different. This is the one of the big differentiating factor between IITian’s and non IITians..The core qualities which i have mentioned above reflects in every IITian’s conversations. The work they do reflects these qualities. so people are curious to know where the person has developed these qualities.. obvious answer is IIT !