This is my 1st Mathematical blog and hence entirely technical one !
The Problem at hand was an old one :
Suppose 1000 men are standing in a circle ; with 1st man holding a gun !
1st man shoots the 2nd guy and gives the gun to 3rd who shoots the 4th
and gives gun to 5th ..........999th shoots 1000th and gives gun back to 1st
whi now kills the 3rd and gives gun to 5th ..... the cycle continues .
Who will be the last Survivor ?!
All varied approaches were tried but answer was reached by 2 ways only
1. Brute force of actually killing 999 people on paper to find the survivor
2.Writing computer program to find the solution
Both were done! 1st by me , 2nd by my friend Shalabh and answers matched 977th person would survive ! Shalabh's program went 1 step ahead , coz it was written for N no. of people !
i.e it accepted how many people did we want in circle of death and calculated the last survivor in each case !
The program made me think and plot the list of survivors against no of people involved in the circle of death! and what followed was beauty of maths revealing itself !
Total no of ppl and No. of the Survivor
( n = m )
n = No of ppl in the circle ;
m = Position of the person who survied the shoot out !
1 = 1st
2 = 1st
3 = 3rd
4 = 1st
5 = 3rd
6 = 5th
7 = 7th
8 = 1st
9 = 3rd
10 = 5th
11 = 7th
12 = 9th
13 = 11th
14 = 13th
15 = 15th
16 = 1st
17 = 3rd
18 = 5th
19 = 7th
20 = 9th
21 = 11th
22 = 13th
23 = 15th
24 = 17th
25 = 19th
26 = 21st
27 = 23 rd
28 = 25 th
29 = 27th
30 = 29th
31 = 31th
The series of odd numbered survivors repeats itself each time growing in a specific way !
1 => 1st cycle 1 = 2^0 element Total =1
1 3 => 2nd cycle 2 = 2^1 elements Total =1+2= 3
1 3 5 7 => 3rd cycle 4 = 2^2 elements Total =1+2+4=7
1 3 5 7 9 11 13 15 => 4th cycle 8 = 2^3 elements Total=1+2+4+8=15
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 => 5th cycle 16= 2^4 element Total=1+2+4+8+16=31 .
.
.
.
The elements in each cycle grow as the power of 2 !
So now according to problem under consideration
n = 1000 ;
Aftr completing 9 cycles of growing odd series
i.e 1+2+4+8+16+31+64+128+256 = 511 elements are done
now cycle having 2^10=512 elements begins ;
n = 1000 corresponds to 1000-511 = 489 th odd no in cycle containing 2^9 elements
(
1000 = 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 489
= 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 489
)
Thus the person having 489th odd no. will survive the shootout of 1000 people !
i.e. (2*489 - 1 ) = 489th odd no. = 977th person will Survive!
Now using above concept, survivor in case of N no. of people in circle of death can be solved
with ease !
Monday, September 7, 2009
Thursday, May 28, 2009
An Analogical Epiphany !
Well I was discussing about the power of Human Imagination , which has been a long time favorite topic of mine to ponder upon , with my doctor and pharmacist friends, which is when the epiphany struck me! The situation under consideration was
"Could a person blind by birth , imagine what was vision or how would it be ? "
To test the power of Human imagination - I wondered
"When such a blind by birth person regains his vision ( due to the wonder of Medical science) , How would what he had imagined vision to be and his actually 1st experience of seeing compare ?"
It would be an enlightenment for him !
Well this topic itself is worth another blog post !
But I want to concentrate on the Epiphany derived from the above discussion !
Taking an analogy from above - if we consider "All the worlds population to be blind and if some one person gains vision - How the hell is he going to explain us ( the rest of the population ) What the phenomena of vision is ? " . He will be helpless in trying to explain us what vision is !! Try doing it yourself. Try and explain Whats Blue yellow and green to a Blind person ! You will realize that You can describe it based on pre-established refrences only ! But if these are not available - U will just have to say - Experience it yourself ; I cant tell you what it is !
Well well that is what has been said about Enlightenment by all the Greats who have achieved it in our history so far ! Experience it yourself ! So Can we dare say enlightenment is a development of a new perception ? of which we initially are bereft of ! Is it like developing new set of sensory organs to perceive something which is non existent for the commons but some few special ones have in history gained it and the no. of such people being so less that we dont have any refrences established of the same ? These special ones have tried to explain to us commoners, about this new perception which they had - in a language and refrences of 5 sensosry organs !! But we simply cant Understand - leave understanding ; we find their talk absurd Coz for us its simply not existent and will be till we EXPERIENCE IT on our own !
The Question to be asked remains that if enough no. of ppl do develop this Perception of Enlightenment in course of Human History- Would we be able to determine accurate refrences of enlightenment like we have of our 5 sense of organs and thus Bring Enlightenment into field of Practicality ?!
"Could a person blind by birth , imagine what was vision or how would it be ? "
To test the power of Human imagination - I wondered
"When such a blind by birth person regains his vision ( due to the wonder of Medical science) , How would what he had imagined vision to be and his actually 1st experience of seeing compare ?"
It would be an enlightenment for him !
Well this topic itself is worth another blog post !
But I want to concentrate on the Epiphany derived from the above discussion !
Taking an analogy from above - if we consider "All the worlds population to be blind and if some one person gains vision - How the hell is he going to explain us ( the rest of the population ) What the phenomena of vision is ? " . He will be helpless in trying to explain us what vision is !! Try doing it yourself. Try and explain Whats Blue yellow and green to a Blind person ! You will realize that You can describe it based on pre-established refrences only ! But if these are not available - U will just have to say - Experience it yourself ; I cant tell you what it is !
Well well that is what has been said about Enlightenment by all the Greats who have achieved it in our history so far ! Experience it yourself ! So Can we dare say enlightenment is a development of a new perception ? of which we initially are bereft of ! Is it like developing new set of sensory organs to perceive something which is non existent for the commons but some few special ones have in history gained it and the no. of such people being so less that we dont have any refrences established of the same ? These special ones have tried to explain to us commoners, about this new perception which they had - in a language and refrences of 5 sensosry organs !! But we simply cant Understand - leave understanding ; we find their talk absurd Coz for us its simply not existent and will be till we EXPERIENCE IT on our own !
The Question to be asked remains that if enough no. of ppl do develop this Perception of Enlightenment in course of Human History- Would we be able to determine accurate refrences of enlightenment like we have of our 5 sense of organs and thus Bring Enlightenment into field of Practicality ?!
Tuesday, February 10, 2009
Religion - the medicine of our wrongdoings ?!
I had the Audacity to watch Sanskaar and Astha Channel together for about 2 hrs at a stretch !
Going through I saw about three Saffron clad bearded babas giving 'discourses' !! Well fine at the face value , but underlying all the 3 satsangs I saw a common thread wherein a dumb looking guy
who doesnt even have an ounce of serenity or piousness on his face sits amidst huge Garlands of flowers , with pictures of Gods and Goddess in the background : with tasteless extravagant and gaudy Decorations - talking anything but Philosophy !
Its fine till here ! I panicked when the the cameraman Panned the camera over the huge crowd that had gathered and was listening to this guy ! Well what was more striking was half of them weren't interested and rest half who were , were not so much interested in listening to this guy as they were in just being present ' at some devotional event' ! Some sort of a mental medicine of 'being present at such an event would wash me off my sins ' !!
When I was a chess Player , I remember a guy telling me " Nowadays I dont get Angry because I have done Advance course of Art of Living " and I was like " OHK !! even I dont get anrgy without even knowing what Art of living is " . All respect to Mr. Sri sri Ravishankar but I want you people to see that this person , doesnt get angry because He has done a Course and not really coz he understood the futility of getting angry !!
People look at religion philosophy and devotion to God not as a way of life but more so of some sort of repair mechanism !! Its same throughout all religions Jesus has suffered for you so you would be free of all your guilt if you follow him , Ganga mein Snan karlo sab paap dhul jayenge , Allah ki marzi ye nahi hua,uske marzi bina kuch nahi hota !!
Come on people grow up , stop treating religion as mental medcine for your wrongdoings !
Going through I saw about three Saffron clad bearded babas giving 'discourses' !! Well fine at the face value , but underlying all the 3 satsangs I saw a common thread wherein a dumb looking guy
who doesnt even have an ounce of serenity or piousness on his face sits amidst huge Garlands of flowers , with pictures of Gods and Goddess in the background : with tasteless extravagant and gaudy Decorations - talking anything but Philosophy !
Its fine till here ! I panicked when the the cameraman Panned the camera over the huge crowd that had gathered and was listening to this guy ! Well what was more striking was half of them weren't interested and rest half who were , were not so much interested in listening to this guy as they were in just being present ' at some devotional event' ! Some sort of a mental medicine of 'being present at such an event would wash me off my sins ' !!
When I was a chess Player , I remember a guy telling me " Nowadays I dont get Angry because I have done Advance course of Art of Living " and I was like " OHK !! even I dont get anrgy without even knowing what Art of living is " . All respect to Mr. Sri sri Ravishankar but I want you people to see that this person , doesnt get angry because He has done a Course and not really coz he understood the futility of getting angry !!
People look at religion philosophy and devotion to God not as a way of life but more so of some sort of repair mechanism !! Its same throughout all religions Jesus has suffered for you so you would be free of all your guilt if you follow him , Ganga mein Snan karlo sab paap dhul jayenge , Allah ki marzi ye nahi hua,uske marzi bina kuch nahi hota !!
Come on people grow up , stop treating religion as mental medcine for your wrongdoings !
Be Rational !
Wednesday, January 21, 2009
Murphy's Law demystified !
" If anything can go wrong in a given situation , it will " - That's Murphy's law, which forms the guiding principle for all the pessimistic bastards in this world ! You all must have got the more comic versions of the same stating , " your nose will itch , when your hands are greasy" or ' cylindrical object falling on floor will roll to the most inaccessible corner " etc. as email fwds.!
Why do we like to believe this shit ? Ahh ! you may say " Who says so , I believe this shit ?"
Well , you may not ! but somewhere inside it sure does click! So thought of analyzing the why does this click ?
The only reason this crap thrives is by feeding on our personal apprehensions and indecisions!
Let me tell you , The Murphy's law will affect you only if you want it to!
when its a 49 -51 situation , this laws tend to give u a morale support to bank upon if you make the 49 as your choice and that's why you want this law to apply so that you can safely curse Murphy and laugh your incapacity off ! Utter crap re ....why would the nature always go against you ? Does it not have better things to do than see to it that you fall! Any guy who ever propounded , publicised or propagated this laws , is a born loser , trying to find an excuse for his incompetence!
Well somewhere for me , this law still click ! Reason ? Simple there's a loser in me somewhere , who wants the solace that I was not responsible for what happened to me !
If you are absolutely confident, there's no place for Murphy or his laws! Does that mean I will succeed if I am confident ? Hell no! That's nature you are dealing with , with its dynamic balance of success and failures ! There is no issue if u fail , but the hypocrisy of laughing it off hailing Murphy is criminal !
So what do I do ? Forget Murphy , Stop being sympathetic to your incompetence, be responsible for and more importantly stop wanting this law to apply to u and it will not !
Why do we like to believe this shit ? Ahh ! you may say " Who says so , I believe this shit ?"
Well , you may not ! but somewhere inside it sure does click! So thought of analyzing the why does this click ?
The only reason this crap thrives is by feeding on our personal apprehensions and indecisions!
Let me tell you , The Murphy's law will affect you only if you want it to!
when its a 49 -51 situation , this laws tend to give u a morale support to bank upon if you make the 49 as your choice and that's why you want this law to apply so that you can safely curse Murphy and laugh your incapacity off ! Utter crap re ....why would the nature always go against you ? Does it not have better things to do than see to it that you fall! Any guy who ever propounded , publicised or propagated this laws , is a born loser , trying to find an excuse for his incompetence!
Well somewhere for me , this law still click ! Reason ? Simple there's a loser in me somewhere , who wants the solace that I was not responsible for what happened to me !
If you are absolutely confident, there's no place for Murphy or his laws! Does that mean I will succeed if I am confident ? Hell no! That's nature you are dealing with , with its dynamic balance of success and failures ! There is no issue if u fail , but the hypocrisy of laughing it off hailing Murphy is criminal !
So what do I do ? Forget Murphy , Stop being sympathetic to your incompetence, be responsible for and more importantly stop wanting this law to apply to u and it will not !
Monday, January 5, 2009
Physical Charoli ( poem consisting of 4 lines )
h μ c
ε G e
I bow down to Thee !
For Sans you I would'nt be !
ε G e
I bow down to Thee !
For Sans you I would'nt be !
Tuesday, December 16, 2008
You cannot fool yourself !
Well if anyone knows yourself , it has to be you !
You know your every thought , every action , every jealousy ,every fantasy !
Everything you wanted the outer world to know not ; is known by you ! There is no pretense prejudice or put up behavior to impress,when its a question of you being your own judge !You can give excuses for your failures or glorify your own success to the outer world, but you know it all what goes behind !You don't need to think twice before saying anything to yourself !You can absolutely be yourself with yourself ! You know what coward you are, when world lauds your courage You know your strengths ,even if world ridicules them as your weaknesses !You can perfectly criticise yourself without tending to demoralization You can pat your back, when u internally know its a Job well done !You cant glorify nor demean yourself in your own mind !You can escape from anywhere but not from yourself !Many a time its this beautiful self of ours ,from whom we run away from ! Coz we cant stand its simple judgment !
On the contrary I would say ~
If ever you find the whole world against you , but this yourself with you !
this yourself in all its simplicity sans the forced attempts to manipulate it
Be rest assured that you are right and will win !
Coz the whole world can be fooled but, You cant fool yourself !
You know your every thought , every action , every jealousy ,every fantasy !
Everything you wanted the outer world to know not ; is known by you ! There is no pretense prejudice or put up behavior to impress,when its a question of you being your own judge !You can give excuses for your failures or glorify your own success to the outer world, but you know it all what goes behind !You don't need to think twice before saying anything to yourself !You can absolutely be yourself with yourself ! You know what coward you are, when world lauds your courage You know your strengths ,even if world ridicules them as your weaknesses !You can perfectly criticise yourself without tending to demoralization You can pat your back, when u internally know its a Job well done !You cant glorify nor demean yourself in your own mind !You can escape from anywhere but not from yourself !Many a time its this beautiful self of ours ,from whom we run away from ! Coz we cant stand its simple judgment !
On the contrary I would say ~
If ever you find the whole world against you , but this yourself with you !
this yourself in all its simplicity sans the forced attempts to manipulate it
Be rest assured that you are right and will win !
Coz the whole world can be fooled but, You cant fool yourself !
Wednesday, December 3, 2008
Why are we Humans Different ?
One of the fundamental law of nature is the Law of equilibrium and stability.
Everything in nature tries to be in a state of equilibrium or a state in which it is most stable.It applies to everything ...from electrons at sub atomic level , to stars @ universal levels !
One handle excess energy in oneself , that excess energy excites us and prompts us to do something so that we can do away with this energy.In humans .....this doesn't apply so aptly.It apparently applies but theres a twist in it ,which makes us different.In our normal lives also we want to live in conditions which are most stable. the stable situation which I say are various ..........mental , social , physical. All of us want to earn a lot of money so that gives us , financial stability. A good character , family etc gives social stability .Having all your parts in working condition gives us physical stability.[My examples for stability may be crude ; but if they make the point clear I wont waste time finding more apt examples] But the twist in the tale comes that humans want to have this stability but they get Bored by it ! There is a constant urge to do something more and seek higher level of stability . Indeed this urge is in all constituents of the nature not only humans but the different is Human try to attain higher level of stability on self initiative !! this is one of the gifts of God I must say , where did this self initiative come from no body knows ,or why is it there , no body knows ?! For example A tiger wont kill another deer if his stomach is full, but human well, he would kill everything in sight and keep it in cold storage for use tomorrow ! Do we call this greed or urge ? A good question . I wouldn't call it greed , greed can be seen in animals also ! but humans its different ! So what is it ? What I am trying to describe here is the fundamental thing which breaks us loose from eat, sleep, reproduce cycle of life followed by all other species on this earth ! If reasoning and logical thinking is the father of exponential evolution of humans as a specie then this urge is definitely the mother ! Another important implication of this urge comes forth if this urge remains inactive for long time ! Put in simple words , I am talking of BOREDOM ! Dogs and Cats never get bored lying around why ? Simple there is no urge to find out higher levels of stability on self initiative in these species ! My friend Pratik had effectively put this human urge in simple words like " Be Happy with What you have .....and still want more !" I am interested in the latter part of the quote coz the 1st part of the sentence deals with contentment with your present ! The "..... Still want more " is what drives us !Its this beautiful coming together of this urge and the ever reciprocation of the logical thinking and reasoning to the demands put forth by this urge which laid down the path of making us unique and the most dominant specie on this planet ! Either one of them missing meant we would be either be busy sharpening the most perfect stone tools or urged for centrally heated caves ,as we sat freezing before the fire !
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