## Tuesday, January 10, 2012

### a2 + b2 = c2

I was going through the problems posted in Project Euler and was suddenly struck with this problem Pythagorean Triplet

Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000

I immediately Googled on how to find Pythagorean triplet and here it goes
Given any two arbitrary numbers ‘m’ and ‘n’
Take a = m2 - n2
b = 2mn
c = m2 +n2
Hence a2+b2 = c2 and we get a triplet

well this method gives an idea how to form new triplets but not to find a triplet containing a given number

I was really interested in this

now consider the expansion (x + a)2 = x2+ a2 +2ax
if a2 + 2ax = some square number .say y2 then we get a triplet ( x, y, x+a )
so for a given 'y' we have to find 'x' and 'a' to get the triplet
( x, y, x+a )
y2 = a2 + 2ax = a ( a + 2x )
a2 = y2 – 2ax
Clearly ‘a’ should be lesser than square root o
f ‘y’

Steps :
1. Divide y2 by 'a'
2. Subtract 'a' from it
3. You shd get an EVEN number else choose another 'a' and goto 1
For eg. take 36… Factors are – 1 2 3 4 6 9 12 18 36
so ‘a’ can take value { 1 2 3 4 }

substituting a = 1 or 3 or 4 we get fractional values of ‘x’ hence we omit them

hence taking a=2 we get x=8
hence the triplet is (8, 6, 8+2) i.e. ( 8, 6, 10)

hence we can generate any triplet for a given number by choosing proper value for 'a'

Furthur observations :

1) 'a' is odd for a given odd square number and vice versa
2) Special case : consider y2= 4 or 1 . there are no values for 'a' in this case as square root are 2 and 1. Hence we cannot have a triplet containing 1 or 2

3) The above statement also proves that "There cannot be a right angled triangle with integer sides and any one of sides equal to 1 or 2"

I Googled on this topic and found nothing regarding this

to be continued

## Monday, January 09, 2012

### The Ultimate Game

Ultimate Frisbee (wiki page), known as Ultimate, is a non-contact, fast-paced field sport played by two teams. The aim is to throw a frisbee (plastic disc) across the field from teammate to teammate, until it is caught in the opponents' end zone (or goal).

This game is very special for me :), for its special at IIM Ahmedabad (it is considered the traditional game here and it is !!) Our team "Flying Dutchmen" play regularly (yeah !! even PGP1s get enough time to play at IIM A) from 11 pm until the number of players reduces below 8. Louis Khan Plaza or LKP is the grass ground of IIM A. It looks decorated only during festive occasions, the convocation and when a game is on !!!

"Whos gonna pull", "Mark your man", "Speed up guys", "Up.. Up.. Up", "Hard D", "SOTG", "Hammer", "Good D", "Bad throw", "Travel", "1.. 2.. 3.. 4.. 5.. 6.. 7.. ... ", "form a stack"..

yeah... its the Ultimate game.. its the one and only Frisbee...

## Saturday, March 19, 2011

### FMS - GDPI

Brief INTRO abt myself

16th March 2011 11 am FMS New Delhi

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PLEASE NOTE : Self attested photocopies needed

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Group Discussion

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Total 2+10+2 mins (last 2 mins for summarize)

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Topic : Poor countries benefit from High end Technology than richer countries

GD went well.. no fish market.. agriculture.. innovative methods needed,, no need high end technology.. define high end technology.. mango iit madras.. fishing methods.. Egypt crisis.. industrial revolution.. india white green gold revolution… !!! many irrelevant points discussed .. some two guys were not given chance to speak.. few dominated…

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Personal Interview

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Panelist : One lady(30+) and two sirs(35+, 25+)

Around 6 mins (what the %^&*)

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Greetings “take ur seat”

Tell me about urself.. _-_-_-_-_-_ I am Raghunath babu from Madurai Tamilnadu .. schooling college. Bhel.. I WAS BORN IN RAMESWARAM ..

(interrupted) speak on PAMBAN BRIDGE (extempore topic) _-_-_-_-_-_ (built by british.. bridge opens to allow ships.. connects Indian mainland to rameswaram island ..ALL STORIES.. said abt its construction.. pillars.. fast construction.. name tamil or sanskrit origin.. real BLA BLAAAAA … felt that I shd not have said reg RAMESWARAM !! )

Why so many ppl from ur college (more than 6 were from my college that day) _-_-_-_-_-_ (said FMS is a good mgmt institute.. many ppl apply to FMS ..!! duno what to say actually..)

What do u do actually in site _-_-_-_-_-_ (answered)

U are working there now ? _-_-_-_-_-_ no sir.. now Chennai project..

(the lady said “U may leave”..!! SHOCKED )

( The sir ) wait.. I have some ques.. u are in which dept _-_-_-_-_-_ project engg dept

( the lady moves out of the chair.. begins to walk behind the panelists and speaks over the mobile loudly..!! what the \$%^& !!! )

ISG what does it stand for. _-_-_-_-_-_ industrial systems group (said abt the business groups in our unit and our products and services )

it means _-_-_-_-_-_ design the project.. Implement it in site..

ok have u used any project mangmt software ? _-_-_-_-_-_ MS project manager

any other _-_-_-_-_-_ Prima vera

have u used it _-_-_-_-_-_ we had a 2 day session on prima vera.. nothing more on it..

work ex certificate _-_-_-_-_-_ sir I am covered under bond and I will be given work ex only after I resign..

bhel will give u money ? _-_-_-_-_-_ no I have to break the bond,,

how much is it _-_-_-_-_-_ one lakh

are u aware of the fees here _-_-_-_-_-_ yes sir around 25000

so u give 1 lakh to do a course for 25k _-_-_-_-_-_ ( said abt FMS and that s a good institute for MBA )

ok fine .. u may leave _-_-_-_-_-_ thank u sir X 2 thank u mam

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PLZ NOTE :

Ur extempore would be based on ur “tell me abt urself” or “anything under the sun” ..!! CAN EASILY DIVERT TO UR FAV AREAS through “Tell me abt urself”…!!

Other Extempore topics given :

1. Deep Blue ( to one guy who was wearing Blue shirt )

2. 2nd to none ( dunno how they gave this )

3. Mediocrity is the center of the Ass ( lol.. no idea )

4. Chair ( guess the chair was dragged !!!! )

5. Girlfriend ( was asked abt the Current girlfriend of Salman Rushdie :D )

6. Breathe of fresh air ( 4 consecutive students from CEG Chennai .. hence this topic given)

7. Victory

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( I felt that I wasted rupees 6k this 6 min interview..!!! I came all the way from blore to delhi for this interview.. they dint care to listen me.. was a namesake interview..!! NO MORE COMMENTS..!! )

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My other GD PI :-)