Lets remember them once again.

I ask you all to chip in and tell which are your "favorite" puzzles, lets remember them and list them all in this post.....

I start with sajals qustion(and i know mayank loves this), where the son whos ship reaches last is the heir and the wise man asks them to switch the ships. simply amazing!!!   sheer awsomeness!!!

Please share you fav. puzzles too.

PS: By the way i have left Monkey Dance for you Mayank ;).

IIT-JEE 2009

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}

And i was right.....

I know i am a little late, but i had predicted Russia's win over holland, and i wud have told u ppl abt this had my net usage not overshooten...Well i guess only my brother stands testimony to that.
Well after the portugeese defeat , i predicted that Russia vs Germany will be the final and ocourse Russia will win.Well i wnt tell the exact reason, bt its NOT any kind of gut feeling.

The Brilliant Mananger

There is a hotel which has infinite rooms. One day, infinite guests arrive and fill those rooms (obviously some rooms would be empty!). Suddenly, at midnight, a VIP arrives and demands a room for himself immediately. The manager of the hotel is not at all worried and arranges for the room in one minute. How is it possible to find one empty room out of infinite rooms in just one minute!?
Level- Easy
P.S. - This puzzle was given to us by our maths teacher while doing the chapter relations and functions!

The CraZy Receptionist

One day, a man walks into a restaurant and asks for water. To his surprise the receptionist takes out a gun and points it to his forehead. Astonishingly, the man says, "Thank you so much!" and leaves the restaurant! Can you explain the situation?
Level - You decide!
P.S.- I heard this puzzle on the radio!

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?

Bloxorz

The link on the right is of a game "Bloxorz". Its a really nice and puzzling game. See if you can cross all its levels.

A paradox

I dunno if you get intrigued by this paradox, but i was and did sone thiking over it(too obvious, after all thiking is what i love to do). However, surprisingly i also came up with some conclusion. i will share that but you opinions first.

Achilles and the Tortoise

Achilles and the tortoise is similar. Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.

Munna Bhaiya Study Tips :: Part 2

Things to Avoid

Things you should start avoiding immediately

Remember that for next 2 years you have to give your best to get admission in a good college. So to take out 55 hours every week, you need to sacrifice some of your time sucking activities.

If you are involved in any of the following activities mentioned below, I suggest you should stop it immediately:

Avoid too much socializing: Avoid too much talking on phone with your friends. Not more than 15-30 minutes every day. Keep yourself away from family discussions. Don’t get into arguments with parents and brothers/sisters. It just wastes your time and energy. Be selfish to focus on your career. Say NO or avoid social functions and visits at relatives.

Avoid long hours on TV, Internet and games: TV serials, movies, matches are real time and energy suckers. If you are too much into TV, cut down immediately. Don’t spend more than 1 hour in front of TV every day.

Internet is the biggest addiction of all time. Real time sucker. Don’t sit on computer for more than 1 hour unless you have to appear for 100percentile tests. To save your time you need to choose TV or Internet browsing or video games. Don’t spend more than 1 hour average daily on any of these activities.

Avoid outdoor sports: Those who are playing physical games a lot should reduce them or should stop them. These games are very tiring. If you are physically tired, you would not be able to concentrate on studies. So for physical activities, I suggest evening walk or light exercise either in the morning or evening.

Avoid night-outs : Those who study late nights, sleep whole day. This is a bad schedule. If you don’t sleep well in the night, you will feel sleepy in school and in your coaching classes. So best is you should sleep for 7 hours any time between 10 PM to 9 AM. Those who don’t get study atmosphere at home in the day time, in worst case they should study till 2.00 AM and get up at 9.00 AM.

Avoid too long or two short sleep hours: It you are sleeping more than 8 hours, stop it immediately. You should target for 7 hours sleep every day. Also avoid day time sleeping for more than 90 minutes. Preferably it should be a nap of 1 hour. Those you could manage to sleep less, I would not recommend a sleep of less than 5-6 hours. If body is tired, mind cannot function properly.

Avoid going to school daily: If you can manage to take school leaves, then you should go school less. But don’t take off from school regularly. I suggest that if possible, go to school not more than 4 times a week. School studies are not going to play important role in your career at this stage. Even school studies should be done just before the exams say 1-2 weeks before exams.

Manmohan Gupta

Munna Bhaiya Study Tips :: Part I

Every day I answer student’s queries related to how they should prepare for IITJEE; how much to study; what to study; when to study and so on.

I have been answering these question since last 13 years when I started teaching Mathematics for IITJEE.

So I decided to start a series of study tips “IITJEE Simplified” where I will write about the best approaches to follow while preparing for IITJEE exam. In this series, I will also answer most common questions that an IITJEE aspirant can come across.

Here is today’s tip:

How many hours should I study at home?

Some of you out there must be toppers of your class or among the top 10% of your class. But that is just a performance in your class or best at a school level. It means till now you have been competing among a small student base of 50 - 1000 students.

But once you start preparing for IITJEE or AIEEE entrance, the competition is huge. This year in 2008, over 3.2 lakh students appeared in IITJEE and over 9 lakh in AIEEE. So my advice is that you seriously need to scale up your efforts to face the competition.

Are you ready for this?

You need to prepare yourself mentally as well as physically to face this competition. Mentally, you need to think wide when you think of competition you are facing. Remember there are more than 10000 schools (just CBSE) in India. So don’t get defocused and remember that you have to compete with unknowns.

Most of you would have scored well in your school level examinations by not even spending 20 hours on studies at home. This is not going to be enough with such a huge competition. You need to scale up your efforts and set a target of 50-55 hours studies at home every week.

But just sitting in front of the books for these 50-55 hours is not enough. You have to study with full concentration, no disturbance, and continuously for 3 hour sessions. The idea is to simulate real exam conditions. While studying, you have to create an atmosphere as if you are sitting in exam. Avoid doing following during a 3 hours session:

• Study on a desk if you have it at home. Avoid studying while lying down on a bed.
• Don’t get up from your desk during 3 hours of study session. Even not for drinking water.
• Don’t listen music during studies. If you have a habit, then slowly come out of it by reducing it day by day.
• No phone calls and no SMS during studies.
• Study with 100 percent concentration as if you are sitting in exam.

Note: to make up 50-55 hours you need to study 6-7 hours every day during the week and remaining 20-25 hours over the weekend.

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?

A Joke

Q. What is a PJ?














A. A 'Phaltoo' Joke.




Q. What is P + iJ?















A. A Complex 'Phaltoo' Joke.




Q. But why don't we laugh at it?













A. Because the 'Joking' part is imaginary!

Updates

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Equilateral Triangle

How can you prove that a triangle is equilateral if and only if
tan A + tan B + tan C = 3√3 ?

Jst fr fun - 2 !

Theory of Equations

Some simple problems... more to follow...

Please scroll to the bottom of the post ONLY after you solve all the questions.

(1) If 2+i√3 is a root of x² + px + q = 0 and p,q are real, then

(p, q) = (__, __).

(2) Solve for x:

| x² + 4x + 3 | + 2x + 5 = 0 where |.| denotes the modulus function.

(3) Solve for x:
sin x + cos x = x + (1/x) where x is expressed in radians. Consider only the positive values of 'x'.

(4) If x² + ax + b = 0 and x² + bx + a = 0 have a common root, find the numeric value of (a+b) if a and b are distinct.

(5) Find the number of solutions of the equation:




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All the above questions are previous years IIT-JEE questions! Surprised, aren't you?

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.

SUDOKU MASTERS 2008

National Sudoku Championship

REGISTRATION OPENS ON SAT 8 MARCH 2008

ONLINE QUALIFYING TEST ON SUN 16 MARCH 2008

FINALS IN BANGALORE ON SUN 30 MARCH 2008

SELECTION OF TEAM REPRESENTING INDIA AT
THIRD WORLD SUDOKU CHAMPIONSHIP (WSC)
TO BE HELD IN HOLIDAY INN RESORT GOA,
14-17 APRIL 2008

Website
http://sudokumasters.in/

Interesting Indeed...

Go to

http://puzzlecodebreaking.50webs.com/rules.htm

to begin.

“ Take nothing for granted. Use every resource you have.....Google, page title, page source, hidden links etc. No information is left accidental. If you think anything doesn't/shouldn't belong to the page, then think again. Many a times, the key to the next step is embedded in the page So, don't trust any piece of information. Besides, your brain should be with you through out the battle. ”

Good luck! Enjoy!

The Appointees

As the Appointment season is on, I have decided to put some appointments on our blog to maintain its standard. Here are my proposals.

POSTS

President :: Sajal Jain
Chief Technical Head :: Ananth Govind Rajan
Director of Innovation :: Shikhar Srivastav
Legal Head :: Shashwat Gangwar
Editor/Co-ordinator :: Mayank Gupta
Member :: Dipanshu Malhotra

DUTIES

The President has to look after all the duties performed by his Cabinet

It shall be the duty of the Technical Head, Legal Head and the Co-ordinator to judge the level of a question. ( 1/2/3/4/5). In case of a dispute, The President shall intervene.
Exciting new concepts shall be proposed by the Director of Innovation.
Technical Head should accomplish the task of maintaining the quality of the blog.
Legal Head has to look after the scores.
Coordinator has to make sure that there is active participation on the blog.(Polls shall also be maintained by him). It is his duty to invite more members to the blog.
The member...hmmm...has to enjoy.

These are just some proposals. Any dispute regarding the same shall be reported as a comment.
If you have some new proposals, please please please post them.

Divisors & Remainders

Two numbers, when divided by a divisor give 4375 and 2989 as the remainder. Their sum, when divided by the same divisor gives 2361 as the remainder. What is the divisor?

If q1, q2 and q3 be the three quotients in the respective divisions, the value of (q1 + q2) - q3 may be:

(a) -2
(b) -1
(c) -0
(d) +0
(e) +1
(f) +2

The question may have more than one possible answer.

One more for you

The value of is

[A].

[B].

[C].

[D]. This question gives us a general trick/method which can be used whenever we have some coefficients in the angle term of cos...x,2x,3x,....,(n+1)x The answer has been posted as a comment.

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

What's probable & what's not?

!!Please comment on the correctness of this question!!

In a lucky draw competition, a contestant had to draw 3 tickets from a pile of well-shuffled tickets. If the numbers on these tickets were in arithmetic progression, he would be adjudged the winner of the contest. If the numbers were not in arithmetic progression, he would return them to the pile. The tickets were numbered from 1 to 201. What is the minimum number of contestants to ensure that at least one of them wins the contest? If 100 people took part in the lucky draw, do you think we could take for granted that at-least one contestant would win the prize?

The Consecutive Numbers

A Math teacher, in order to keep two of her students occupied thought of two consecutive numbers in the range 1 to 10, and told one of the students Alex one of the numbers and the other student, Sam the other.

Sam and Alex then had the following conversation:

Alex: I don't know your number.
Sam: I don't know your number, either.
Alex: Now I know!

How many such sets of numbers can you find? Can you find all the sets which could have been thought up by the Math teacher?