The Hardest Logic Puzzle in the World

Blue Eyes


A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?


There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

A real Puzzle

There is a desert of 1000km stretch. The two endpoints are A and B. A camel is standing at A and there are 3000 bananas. The camel can carry a maximum of 1000 bananas on his back. The camel eats 1 banana for travelling 1km. Now the problem is to find the maximum no. of bananas the camel can carry from to B.

A mathematical question

A man is initially standing at a certain point A. He starts walking 100 metres towards the east, then 50 metres towards the north, then 25 metres towards the west, then 12.5 metres towards the south, then 6.25 metres towards the east, then 3.125 metres (half of the previous distance) towards the north, and so on. Finally, He reaches a final point B after repeatedly walking in this fashion. What is the distance between points A and B?

Perfect in limits...hmmmm?

I think you have attained mastery in limits. So try out the following two problems..Similar but quite different......and please don't hesitate to comment...

So here they are:

1.

2.

I think its obvious that the answer is not obvious!

Elements - Periodic Table Song

Visit this link

Listen and enjoy
Its fun

Tricky number

Find out a 10 digit number in which 1st number denotes number of 0's in it , 2nd number denotes number of 1's in it , so on and 10th number denotes number of 9's in the number. find the number

The number is unique

{Bit of logical + mechanical}

Congratulations

Well , I just saw the bottom of the blog where it is mentioned that the site has been online since 10th May 2007
So congratulations to all of us for keeping this radical blog alive for more than a year. This blog is really a proud achievement of all of us.
What do you think?

Crazy Questions at Google Job Interview

Many are open ended with several right answers and many I haven't been able to answer, therefore I did not provide the answers.

1. How many golf balls can fit in a school bus?....(Good Question)

2. You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?

3. How much should you charge to wash all the windows in Seattle?....(Good Question)

4. How would you find out if a machine’s stack grows up or down in memory?

5. Explain a database in three sentences to your eight-year-old nephew....(not relevant for us enough!)

6. How many times a day does a clock’s hands overlap?

7. You have to get from point A to point B. You don’t know if you can get there. What would you do?

8. Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

9. Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?

10. In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

11. If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

12. If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

13. Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it�s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?....(remember class 10th quiz)

14. You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?(My answer....No)

15. How many piano tuners are there in the entire world? (piano tuners...????)

16. You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?...simple

17. You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)....already posted

2=1 ?

First Way to prove it.
(n+1)^2 = n^2 + 2n + 1
or, (n+1)^2 - (2n+1) = n^2
subtracting n(2n+1),
or, (n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)
or, (n+1)^2 - (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 - n(2n+1) + 1/4(2n+1)^2
or, (n - 1/2)^2 = (n + 1/2)^2
or, (n - 1/2) = (n + 1/2)
or, -1/2 = +1/2
or, 1 = 0
or, 2 = 1 !!


Second Way

4*4 = 4 + 4 + 4 + 4

:. 4*4= 4 + 4 +… 4 times.

:. x*x = x + x + … x times.

Differentiating,

2*x = 1 + 1 + 1 … x times.

:. 2*x = x

Hence 2 = 1!!!

Third Way

Every1 here knows the pretty little Binomial thorem going as :

(a+b)n = an + n*b*an-1 + ... + n*bn-1*a + bn
Observing we find that leaving the first and last term, all other terms are a multiple of n.
For some wierd results, let us put n = 0 ;
LHS = (a+b)0 = 1
RHS = a0 + 0 ... + 0 + b0
= 1 + 0 ... 0 + 1
= 2
:. since LHS = RHS
2 = 1

Fourth Way
- 1 = - 1
or, sqrt(-1) = sqrt(-1)
or, sqrt(-1/1) = sqrt(1/-1)
or, sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
or, i/1 = 1/i
or, i2 = 1
or, -1 = 1
or, 2 = 0
or, 1 = 0
or, 2 =1

Fifth Way

The very interesting infinitie series :

0 = 0 + 0 + 0 + 0 ...

For those who don't find it so interesting, follow me.

0 = ( 1 - 1 )
:. 0 = ( 1-1 ) + ( 1-1 ) + ( 1-1 ) ...

Now all of you would have paid attention in primary school when we were taught the associative law of addition.
Interestingly applying that here,

0 = ( 1-1 ) + ( 1-1 ) ...
or, 0 = 1 + (-1+1) + (-1+1) ...
or, o = 1 + 0 + 0 + 0 + 0 + ...
or, 0 = 1
or, 1 = 2

Sixth Way

- 20 = - 20

or, 25 - 45 = 16 - 36

or, 5² - 5*9 = 4² - 4*9

or, 5² - 5*9 + 81/4 = 4² - 4*9 + 89/4

or, (5 - 9/2)² = (4 - 9/2)²

or, (5 - 9/2) = (4 - 9/2)

or, 5 = 4

or, 2 = 1

The question is, Can you find another way of proving it?

Jst fr fun - 2 !

Jst fr fn!

Don't you think that I was influenced by today's assembly.

In an attempt to keep the blog alive though I have changed the blog's purpose.

Two good syllabus questions

1

Quadratic Equations

If α, β, γ, δ are the four positive roots of the equation x⁴ -12x³+ax²+bx +81=0, then find “a” and “b”.

2

Permutations and Combinations

Find all possible arrangements of the word "COMBINATORICS" such that all the vowels are in alphabetical order and consonants are also in alphabetical order.

Note: Consonants and vowels to be considered separately.

Note: These are not puzzles but JEE-level questions

Sequence 2

Find the next term of the sequence:
1, 2,6,12,25, _


Hint: The answer is in 40's or 50's

Please give the logic as well as logic only would decide the correctness of the answer.

Some more CJ's, SJ's, JC's to make you CRY

I think you are familiar with the term CJ, ie, "Chhonkar Joke" another name for low level(extrreeeeemely low level) sastas..

I have posted these on the blog "Puzzle Spot" because they also involve certain(very different) kind of thinking and presence of mind

Note:Comments are necessary for this post.
I would like you to consider my decisions which I have made upon the level of a PJ after much technical review. However if there are any discrepancies I would consider them.

Here are some. Some are better than CJ so consider them as SJ(Shikhar Joke) and some are even better so you can consider them as JC(Jain Comments)..


Question: An elephant was in love with a she-elephant. But the she-elephant
went and got married to some other elephant. So our elephant was very
Depressed. One of his friends felt sorry for him, and took him to a park to
cheer him up. In the park, they sat on a see-saw, but the see-saw broke.
Now, which song would our hero sing?(CJ)





Ans: "See-saw ho ya dil ho, aakhir toot jaata hai."



Question: Two hairs on a bald man's head fall in
love with each other and want to get married, but
cannot. Why?(SJ)






Ans: Because under Indian laws, "baal vivaah" is
illegal.


Question: One fine morning, Ravan felt guilty day
for all his bad deeds. He felt that he should go an
apologise to Ram for all the problems he had caused. So he went to Ram's
house and knocked on the door. Ram opened the door and was surprised to
find Ravan standing there. Ravan just kept staring and thinking but
didn't say a word. What was he thinking?(JC)





Ans: "Kis mooh se maafi maangoon?"


Question: How do you "cut" roads?(CJ)






Ans: By laughing... because "Haste haste cut jaye
raaste".


Question: Luv and Kush are going to a village and pass by a well. Luv falls
into the well. Why?(SJ)






Ans: Because Luv is blind.


Question: Now, Kush also jumps in. Why?(CJ)






Ans: Because Luv ke liye saala Kush bhi karega!



Question: Jackie Chan ki saas ka naam kyahai? Socho, socho. Nahi pata?(JC)






Ans: D'Cold; Because... Chan ki saans - D'Cold


Question: Chalo ab batao, Jackie Chan ki bahu ka
naam kya hai??(CJ)









Ans: D'Cold again... Kyunki saans bhi kabhi bahu thi


A railway station beggar meets another beggar. A software engineer meets
another software engineer.
Both of them ask the same question to each other.
What is the question?(DJ)-Dipanshu Joke







"So, which platform are you working on?"

A large ssssssssss noise should be produced right at this moment


Question: What do you call a person who is leaving
India?(CJ)




Ans: Hindustan Lever.


Question: What do you call a person who leaves India, but doesn't travel
much?(DJ)





Ans: Hindustan Lever Limited.



Question: In an elephant school, some loafer elephants were hanging around
in the canteen. A sexy female elephant passes by. What do the loafer
elephants say about her?(CJ)






Ans: Look yaar, 36000 - 24000 - 36000!!


Question: Kalidas ka ek bhai joote banata tha. Uska
naam kya tha?(DJ)






Ans: Adidas.


Question: Prasad asks Kumble to bring a Pepsi. Kumble brings a bottle, but
takes it directly to Tendulkar. Why?(JC)





Ans: Because Tendulkar is an opener.


Question: What is the similarity between Satynarayan pooja and the Indian
cricket team?(AGRJ)-understandable






Ans: Dono ke ant me "Prasad" aataa hai.

Question: Who is Joe?(CJ/DJ)







Ans: Kambakth ishq... Because "Kambakth ishq hai
Joe!"


Question: The Madrasi said, I want to see the movie "my heart is an
umbrella'. Which movie did he really want to see?(AGRJ)







Ans: Dil Chhaata Hai.


Woh kaun sa hindi geet hai jis main "Internet Explorer" ka zikar kiya gaya
hai???(DJ)


Hint: The heroine also refers to herself as Internet Explorer.







The answer is... Maine Pyar Kiya.

And the song goes....

Aajaa shaam hone IE (Internet Explorer)
Mausam ne lee angada IE
To kis baat ki hai lada IE
Tu chal........ Main IE !!!




Once 5 CHIPKALIs (house lizards) :
Phulwa,RaamPyaari, RaamDulari,RaamPuri and
RaamChuri were crawling on the wall when all of a sudden, Phulwa started to
sing a song. the moment Phulwa stopped singing the song, RaamPyaari,
RaamDulari, RaamPuri and RaamChuri fell down from the wall !!!... WHY ???(SJ)









coz, they all started clapping !!!!


PJ Isse kehte hain.........

Gattu ek lecture attend karta hai. lecture ke baad use bhookh lagti hai. so
he goes to the canteen. Canteen mein gattu ek pav leta hai. jaise hi woh
pav khane ke liye uthata hai to dekhta hai ki uski plate mein "jannat"
likha hai.

To janaab ab aapko yeh batana hai ki gattu jiska lecture attend karke aa
raha hai, us proffessor kanaam kya hai??? guess(JC)









The answer is

Ishq Ki Chhaon.

Jinke "Sir" ho "Ishq ki Chhaon"
"Pav" ke neeche "Jannat" hogi....

Don't scratch ur head this is a song from film "Dil Se"









What wud u call a Gal who never laughs ????(CJ)










....and the Answer is..........

HASINA !


Once all the scientists die and go to heaven. They decide to play
hide-n-seek. Unfortunately Einstein is the one who has the den. He is
supposed to count up to 100 ...and then start searching. Everyone starts
hiding except Newton. Newton just draws a square of 1 meter and stands in
it rightin front of Einstein. Einsteins counting....
97,98,99.....100........


He opens his eyes and finds Newton standing in front.
Einstein says "newtons out..newtons....out....." Newton denies and says i
am not out. He claims tht he is not Newton. All the scientists come out
and he proves tht he is not Newton...... how ????(JC)



lesson from this PJ- use of physics is not limited








His proof:

Newton says:


I am standing in a square of area 1m square. That means I am Newton per
meter square. Hence I am Pascal....since Newton per meter square = Pascal

Think Free – Your Office Online!!

ThinkFree Online is an Internet-based file sharing and storage ( Java Application).
You'll get 1Giga for free to storage any file you need. (up to10MB for a file)

The platform allows you to:

1. Create Microsoft Office compatible word processing, spreadsheet and presentation files or edit existing documents.
2. Access your most important documents and applications from any computer anytime.
3. Share your inspiration with others - Set the privilege for each person, allowing them either read only or read and edit.
4. Document revision history and rolling back-ThinkFree Online tracks previous versions of a document.
5. Publish live documents within your blog or publish your files to a location on the internet. Send private message/email to your friends when you publish new documents.
6. Add to your work: images, graphs, charts and input from others. Moreover, you can add images from Flickr to your documents.
7. Create your own guest book.
8. Add comments and Tags.

Unfortunately the application is a bit heavy because of the Java but the results are pretty good and the interface is pleasant to use.

ThinkFree Office is compatible with Windows, Macintosh, Unix and Linux systems.

Once Again, the Same Puzzle

Find the number of integral solutions to the following equation.
1/x + 1/y = 1/12

The Comparision of The TITANS

Have a look at this greatest comparision between the 2 most popular teams in the world





An Effort By:

Sajal Jain
Shikhar Srivastav

Weigh It

Suppose five bales of hay are weighed two at a time in all possible ways. The weights in pounds are 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121.

How much does each bale weigh?

Level:Medium

Flowers

In a small town, there are three temples in a row and a well in front of each temple. A pilgrim came to the town with certain number of flowers.

Before entering the first temple, he washed all the flowers he had with the water of well. To his surprise, flowers doubled. He offered few flowers to the God in the first temple and moved to the second temple. Here also, before entering the temple he washed the remaining flowers with the water of well. And again his flowers doubled. He offered few flowers to the God in second temple and moved to the third temple. Here also, his flowers doubled after washing them with water. He offered few flowers to the God in third temple.

There were no flowers left when pilgrim came out of third temple and he offered same number of flowers to the God in all three temples. What is the minimum number of flowers the pilgrim had initially? How many flower did he offer to each God?

Level:Easy

Some of the classics of KVPY

1) How many 4 digit square numbers exist such that after increasing each digit by 1 we get another square number?
2)3 points lie in the x-y plane such that coordinates are (0,0),(6,0),(2^1/2,3).Find the largest side of the square inscribed in it such that the 2 vertices's of square lie on AB(x-axis).
3)A circuit diagram is drawn with 1 ohm resistance lying along the sides of a cube and a 10v battery is connected to it. Find the current in the circuit.
4)A light ray is sent from vertex A of a square making an angle "theta" with the side AB. The ray after being reflected from side BC,CD,DA passes through vertex B. Find sin"theta".

To Shikhar and Ananth,
Anybody solving all 4 correctly deserves a treat from me.

If you have any confusion regarding any question please comment.