Sunday, December 30, 2007

The King and the Poison Puzzle

The King and the Poison Puzzle
In a far away land, it was known that if you drank poison, the only way to save yourself is to drink a stronger poison, which neutralizes the weaker poison. The king that ruled the land wanted to make sure that he possessed the strongest poison in the kingdom, in order to ensure his survival, in any situation. So the king called the kingdom's pharmacist and the kingdom's treasurer, he gave each a week to make the strongest poison. Then, each would drink the other one's poison, then his own, and the one that will survive, will be the one that had the stronger poison.

The pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer's plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. When the time came, the king summoned both of them. They drank the poisons as planned, and the treasurer died, the pharmacist survived, and the king didn't get what he wanted.
What exactly happened there?
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Sunday, December 23, 2007

What's Special About This Number?

I was wondering when i came across this page is to whether really a number has its own identity. If it does, how many such numbers would be there, a few hundreds?? thats it and definitely not in order. But this definitely changed my view and perceptions. This is guy is very into numbers and really puzzled me up on how would he had found these all.

The list contains the speciallity of first 10,000 numbers. Imagine that the numbers from 0 to 9999 have their own identity. They can be attributed to their own special property. To list a few here are some. To go through the complete list visit What's Special About This Number?. Take a look each has a context reference too. Definitely a hell of work and dedication by the owner.

0 is the additive identity.
1 is the multiplicative identity.
2 is the only even prime.
3 is the number of spatial dimensions we live in.
4 is the smallest number of colors sufficient to color all planar maps.
5 is the number of Platonic solids.
6 is the smallest perfect number.
7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
9 is the maximum number of cubes that are needed to sum to any positive integer.
10 is the base of our number system.
11 is the largest known multiplicative persistence.
12 is the smallest abundant number.
13 is the number of Archimedian solids.
14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.
15 is the smallest composite number n with the property that there is only one group of order n.
16 is the only number of the form xy = yx with x and y different integers.
17 is the number of wallpaper groups.
18 is the only number that is twice the sum of its digits.
19 is the maximum number of 4th powers needed to sum to any number.20 is the number of rooted trees with 6 vertices.
21 is the smallest number of distinct squares needed to tile a square.
22 is the number of partitions of 8.
23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.
24 is the largest number divisible by all numbers less than its square root.
25 is the smallest square that can be written as a sum of 2 squares.
26 is the only positive number to be directly between a square and a cube.
27 is the largest number that is the sum of the digits of its cube.
28 is the 2nd perfect number.
29 is the 7th Lucas number.
30 is the largest number with the property that all smaller numbers relatively prime to it are prime.
31 is a Mersenne prime.
32 is the smallest 5th power (besides 1).
33 is the largest number that is not a sum of distinct triangular numbers.
34 is the smallest number with the property that it and its neighbors have the same number of divisors.
35 is the number of hexominoes.

Complete list at.... What's Special About This Number?
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Wednesday, December 19, 2007

The Recruitment Puzzle - Cool motivations.

Recruitment has now become a game , an approach or a puzzle. The interview is based on how a person can think in different ways. And so is the company Look at the following advertisements of the companies announcing the openings in their company. A great motivation to join a company, if they think this much for an advertisements / billboards , they sure must be interesting to join and rather more interesting to work for them.

Lets take up the challenge and look through these state of the art advertisements:

1.


2.


*Answer: "Now Hiring" in ASCII
3.


4. Ad for a job found in
Manhattan Craigslist (click for enlarge)




5.


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Sunday, December 16, 2007

Solution to Vandal Puzzle

This is the solution to the puzzle The Vandal Puzzle - The Ug and the Mug published on 20th November. Those who haven't yet tried the puzzle Click here!!

And here goes the Solution/Answer to the Puzzle:
There is no way that Ug and Mug can produce 2000 pieces of glass starting from one piece, and smashing any piece into 7 or 10 pieces.

We can show this by showing that there is a special property that one piece of glass has, which is not changed by being struck by Mug or Ug, or more precisely, which is also a property of the number of pieces of glass resulting after a strike.

To understand how this argument works, suppose a simpler case, that a single vandal named Bug can smash one piece of glass into 3. Now can he ever create 100 pieces of glass? If he takes one of the 3 pieces of glass and smashes it into 3, then he has now a total of 5 pieces. Choosing any one of these pieces and smashing it yields a total of 7, and so on. Every one of these numbers is odd. This is no accident. If you start with an odd number of pieces (which we did), take one and make it three, you have increased your original number by 2, which leaves it odd. Since you can't get from 1 to 100 by hops of size 2, Bug can't make 100 pieces by starting from 1.

Now we note the Ug and Mug have a similar problem. Each strike by Ug increases the number of pieces by 6, while Mug increases the number by 9. Both of these numbers are divisible by 3. That means that adding them to the current total of pieces cannot change the remainder of the total, when it is divided by 3. This remainder is called an invariant. The number 1 has a remainder of 1 when divided by 3. Therefore, at any time during Ug and Mug's spree, the total number of pieces of glass must have a remainder of 1 when divided by 3. The number 2000 does not have this property, and so it is not possible for them to create this number of pieces.
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Friday, December 14, 2007

Origin of Google ... The Googol Inc.

For people wondereing what the thing , the big name GOOGLE means. Is google really a word and if it is what does it mean. Many years ago this word ceased to exist and never ever had a meaning. With the coming up of Google, its now the most known word for internet users. A person starting to learn internet first learns how to use google. Yeah.. the story not behind the Google but being Google as compiled by David Koller is as
In 1996, Larry Page and Sergey Brin called their initial search engine "BackRub," named for its analysis of the web's "back links." Larry's office was in room 360 of the Gates CS Building, which he shared with several other graduate students, including Sean Anderson, Tamara Munzner, and Lucas Pereira. In 1997, Larry and his officemates discussed a number of possible new names for the rapidly improving search technology. Sean recalls the final brainstorming session as occurring one day during September of that year.


Sean and Larry were in their office, using the whiteboard, trying to think up a good name - something that related to the indexing of an immense amount of data. Sean verbally suggested the word "googolplex," and Larry responded verbally with the shortened form, "googol" (both words refer to specific large numbers). Sean was seated at his computer terminal, so he executed a search of the Internet domain name registry database to see if the newly suggested name was still available for registration and use. Sean is not an infallible speller, and he made the mistake of searching for the name spelled as "google.com," which he found to be available. Larry liked the name, and within hours he took the step of registering the name "google.com" for himself and Sergey (the domain name registration record dates from September 15, 1997).
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Sunday, December 9, 2007

The Inadvertent Glossary of College - A revival... Revisited

IIT Delhi - My CollegeIIT KharagpurIIT Bombay

Earlier posted without meaning.. now have them.. Take a look

After the college, i remember the college language the most. I took this initiative earlier to create a glossary for all those unscrupulous words, but all those gone with the wind with the end of college's last day. So i have started the compilation once again.
This isn't actually a glossary of the words but only a list from my IIT days.
I invite all other students and "ex-students" to add their words as comments underneath. Also do add your version of meanings for the words you give and already given here.
A comprehensive version of the glossary is on its way. So do contribute to the glossary and ahhh well .. a contri to your cccccccooooooooooooooooooooollll days.... college days!! Do name your college dudes /dudettes
Please do add the funny names you gave to your friends with the serendipity behind the name

So here we go : currently the INADVERTENT GLOSSARY OF IITIANS with meainings - A LINGO to REVIVE

attachee - The day scholars. Origin - The students are either "allotted" or are "attached" to a hostel. Allotted students live at the hostels or are hostelites while the attached students are represented by the attached hostels for all events and competitions.
abs – Absolute achievement for a work. Most generally when a student gets the maximum marks obtainable in an exam
arbit – Arbitrary. Generally used for arbitrary work done/ comments passed by a person
bakait – The person performing bakaiti
bakaiti – Drastic version of timepass with no results and no reason.
bakar – synnonym for bakaiti
bakchod – Person who is highly involved and is fond of bakaiti
banda – A boy
bandi – A girl
batti – Electrical department
bhatke – The B.Tech students.
compu – Computer science department
contri – Contribution. Generally used for the contribution based parties/outings.
d00d - Elated version of Dude.
dabbe wala – Person with computer or a student of computer science department
dayski – Day scholar
depc – Department change
despo – Desperate person, Generally for girls
DISCO - The Disciplinary committee of IIT.
fattu – Person who fears for doing anything he is asked to or he needs to
fight marna – Trying hard on doing something
fighter – Person trying hard on everything
fod dalna – Excelled with flying colors in something
frustaapa – Act of showing Frustration
frustu – Frustrated person. Generally used for a person desperate for girls
fukka – Failed in an exam or more appropriately getting F-Grade in an exam
full toss – Student who happened dropped any year before graduation
fultoo – On full swing
funde – Advices/Fundamentals of a person.
fundoo – Highly impressing
gadda – Seriously foolish person
HFC - Holistic Food Centre
Holistic – HFC – Holistic Food Centre
ic – Institute C……. Generally used for a person considered as worst student in the college
insti – The institutional area. Generally the place where classes take place
janta – People involved
load – Tension arising due to some work or act of someone
maggu – Highly studious person
mast – Interesting and enjoyable. Better called as cool.
matke – The M.Tech students.
max – Maximum. Generally used for the high enthusiasm of a person
ms – Main structure. The highest building in IIT delhi
mugai or magai – Studying.
pain maarna – 1. Unnecessarily trying for something, 2. Frustrated by something
RR – Reading room
senti – The feeling of getting Sentimental.
sponti – The spontaneity of the person regarding any thing he/she does.
stud – The Person expert/ excel
studaapa – Act of showing perfection/excellence/ stud things
Sutta - Cigarette / Smoking
tapna – Look out for girls
tappa – Student who dropped an year or more before graduation
timepass – Just for passing time
waat – Had worse of all the things
WindT – Wind tunnel in IIT Delhi
ZeroX – hell of the famous version of XEROX shop at IIT DELHI
zukk – Zero marks

CONTRIBUTRIONS

kirtan added:
NBD :- Its actual meaning is Nervous Break Down, but this term is used generally whenever any1 is scene in tension or thinking about something
(for more details, you may contact some IITB Junta)
NBDU :- one who found in NBD very often

uncommon common added:
rattafication meaning "act of learning without understanding a single thing".

mohit added:
ghissu - highly studious person..
ghisai - act of studying
bond - an expert in any field...
bondappa - showing off the bond inside you
chutiyappa - do some chutiya stuff..
facha - first yearite male
fachi - first yearite female
Andhra - all the southies..
god - expert in any field..
hadd - anything extreme
diro - director

heres sm lingo related more to IITG -
SAC - sport activity centre
NAC - new acedemic complex
CC - computer centre
TC - transit complex
khokha - faculty gate market
chinky - d local gals for thier assamese looks
localite - neone belonging to d northeast
dosa - dean of student affairs

HEY PEOPLE PLEASE DO ADD , IF I FORGOT SOMETHING HERE!!! I AM WAITING!!!


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Thursday, December 6, 2007

The Ant's Puzzle

Problem with Ants Puzzle
The noted gourmet Pangolini Aardvark is preparing a late night snack of "Ant au Chocolat" and "Ant au Fromage". This requires the use of a five foot pole. One end of the pole is over a bucket of melted chocolate and the other is over a bucket of melted cheese.

Pangolini sprinkles some ants onto the pole. They immediately start scampering along the pole in random directions. If two ants run into each other then they both instantaneously reverse their directions and are now moving away from each other. An ant can change direction many times. Eventually, all of the ants will fall off one or other end of the pole. If each ant travels at a speed of one inch per second, what is the maximum time until all ants have fallen off?

Suppose now that n ants are placed on a circle of five foot circumference and randomly choose their direction of travel and again reverse direction when they bump into each other. One of the ants is named Alice. What is the probability that Alice is back where she started, one minute after the ants start their scampering.

Back to the pole. Alice starts in the middle of the pole. There are n other ants placed randomly on the pole and they start scampering in random directions. Alice has a cold. When an ant with a cold bumps into another ant, the uninfected ant catches a cold too. What is the expected number of ants who catch cold before they all fall off the pole?

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Saturday, December 1, 2007

Solution to Adultery Puzzle

This is the solution/answer for the Adultery puzzle posted on 29th October 2007.
Those who havent tried it yet.. Give it a try at Adultery Puzzle

If there was only one cheating husband, then on the day of the announcement, 999 wives would know there was one cheating husband, as they had already assumed; one wife, the one being cheated on, thought there were no cheaters, and now knows there is at least one. Hence, she realizes, it must be her husband who is cheating. So she turns him in.

Suppose instead there were two cheating husbands. On the first day, 998 wives know what's up; wife #999 knows that husband #1000 is cheating, and wife #1000 knows that husband #999 is cheating. They both expect the one cheating husband to be executed. But neither one turns in their own husband, so nothing actually happens. Thus, after the executioner gets no offers, both wives realize that the only explanation is that there must be two cheating husbands, not one. So on day 2 there is a double execution. Reasoning this way, for our original problem, on the 50th day, all 50 cheated wives realize that their own husband is a cheater, and all 50 husbands get the chop.

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