Probability in air

Source:Peter Winkler “Mathematical Puzzles. A Connoisseur’s Collection”,
published by A.K. Peters, Ltd. in 2004.


Problem:
100 people board an airplane with 100 seats. Each person has a seat assigned. For
Some reason, the 1st person who gets in takes her seat at random. Then the 2nd
passenger takes her seat if it is not occupied (by the 1st), and picks a seat at random
if her seat is occupied. Then the 3rd passenger takes her seat if it is not occupied
(by the 1st or 2nd), and picks a seat at random if her seat is occupied. And so on.
What is the probability that the last person will sit in her seat?

Russian Olympiad

Source: Russian Mathematics Olympiad Problem 8th Grade.
Taken from Tanya Khovanova's blog

Problem: How many negative roots does the equation x4 − 5x3 − 4x2 − 7x + 4 = 0 have?

Sum to prove

Source: http://www.math.udel.edu/~lazebnik/papers

Problem:
Consider any positive integer N whose (decimal) digits read from left to right are in
non-decreasing order, but the last two digits (tens and ones) are in increasing order.
Prove that the sum of digits of 9N is always exactly 9.

Resources

A fun read................

Surprises !Surprises !Surprises ! 

Another Grid

Source : Some random website

Problem: Find the missing number

7	4	8
3	9	7
6	5	10
?	8	4

Which way bus is moving?

Source: Pre School test question,which most adults fail

Problem:
Which way bus is moving?

(I failed it too.) :p

Number of handshakes

Source: Some random quant book

Problem:
At a party, everyone shook hands with everybody else.
There were 66 handshakes. How many people were at the party?

Fish in the pond

Source: CAT 2011 question(I couldn't solve it)


Problem:

Suppose you have a pond and in that pond you have some goldfish. Size of all the fish is same and they are evenly distributed in the pond.
You want to count them. You threw the net inside the pond and saw that there are 40 fish in the net. You marked all of them with blue color.
You repeated the same activity and this time you got 60 fish out of them 4 had the blue color mark on them(it means they were from the first withdraw).

What is the approximate number of fish in the pond?

Series

Source: Quant company written test

Problem:

11, 12, 26, 79, 81, 163, 491, 492, ?

Parity

Source:Source: Mathematical Circles -Dmitri Fomin

Problem:
Pete bought a notebook containing 96 pages and numbered them from
1 through 192.Victor tore out 25 pages of Pete’s notebook and added the
50 numbers that he found on the pages. Could Victor have got
1990 as the sum?

Probability Again

Source: Surprises by Felix Lazebnik


Problem:
Write two distinct integers, one on a card, and put two cards on the table face
down. You can pick any of the two, look at it, and then you have to guess whether
the other number is larger or smaller. Prove that you have a strategy to make a
correct guess with probability strictly greater than 1/2.

The ten digit number

Source: Bhupesh Bhargav, Algo Embedded Systems

Problem:

Find a 10-digit number, where the first figure defines the count of zeros in this number, the second figure the count of numeral 1 in this number etc. At the end the tenth numeral character expresses the count of the numeral 9 in this number.

Gatekeepers of Nalanda

Source: Ancient Indian Riddles http://bronze.uco.edu/

This riddle was used by the gate keepers of the Nalanda university as the
entrance test question(Nalanda was the first completely residential university
of the world to have entrance examinations, and the gate keepers used to be
most sound brains of the campus who tabbed the entrance of the candidates)

Problem:

A spirited jig it dances bright,
Banishing all but darkest night.
Give it food and it will live;
Give it water and it will die.

Bacteria population

Source: Quant company interview puzzle

Problem:

A Petri dish hosts a healthy colony of bacteria.
Once a minute every bacterium divides into two. The colony was founded
by a single cell at noon. At exactly 12:43 (43 minutes later) the Petri
dish was half full. At what time will the dish be full?

Hint: You can get the solution in Half a second  \m/ if you won't think arbit.

Egg Breaking strategy

Source: Google Interview Puzzle

Problem:
With two eggs and a building with 100 floors,
what is the optimal strategy for finding the lowest floor at which an egg
will break when dropped?

http://www.scribd.com/doc/7217370/Egg-Puzzle-Generalized-Solution-for-Any-Number-of-Eggs

Grid Computing

Source: Algorithm analysis -Coreman

Problem:

A room has n computers, less than half of which are damaged. It is possible to query a computer about the status of any computer. A damaged computer could give wrong answers. The goal is to discover an undamaged computer in as few queries as possible.

Twist

Source : Asked by a fellow Headstrong

Problem: Why I like Ulan Bator?

General's Army Attack

Source: Delightful Puzzles ,Gurmeet Manku of google

Problem:

Two armies, each led by a general, are preparing to attack a city. The armies are encamped outside the city on two mountains separated by a large valley. In order to capture the city, the generals must attack at exactly the same time. The only way for the generals to communicate is by sending messengers through the valley. Unfortunately, the valley is occupied by the city's defenders, so there's a chance any given messenger will be captured. Each general has no way of knowing if their messenger arrived. How do the generals coordinate their attack?

Defective Solutions

Source: Sharygin Geometry Olympiad by Zaslavsky, Protasov and Sharygin.


Problem:

Find numbers p and q that satisfy the equation: x2 + px + q = 0.The book asks you to find a mistake in the following solution:

By Viète’s formulae we get a system of equations p + q = − p, pq = q. Solving the system we get two solutions: p = q = 0 andp = 1, q = −2.What is wrong with this solution?

Hungry Camel

Source: Bhuesh Bhargav,Algo embedded systems

Problem:

Lukas have a banana plantation and a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 kilometer. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.

What is the largest number of bananas that Lucas can deliver at the market?????

The Greengrocerer

Source: Bhupesh Bhargav ,Algo Systems

Problem:

On a sunny morning, a greengrocer places 200 kilograms of cucumbers in cases in front of his shop. At that moment, the cucumbers are 99% water. In the afternoon, it turns out that it is the hottest day of the year, and as a result, the cucumbers dry out a little bit. At the end of the day, the greengrocer has not sold a single cucumber, and the cucumbers are only 98% water. How many kilograms of cucumbers has the greengrocer left at the end of the day?

Magnetism

Source: H C Verma's Fundamental of Physics

A very common one!!! 

Problem:
You are in a room with no metal objects except for two iron rods.
Only one of them is a magnet.
How can you identify which one is a magnet?

Tailor's trailer

Source: Bhupesh Bhargava of Algo Systems

Problem:
A tailor with a real fancy for cutting cloth has ten pieces of material.
He decides to cut some of this material into 10 pieces each. He then
cuts some of those resulting pieces into ten pieces each. He continues this
way until he finally tires and stops. He counts the number of cloth pieces;
after a few minutes he determines that there are 1984 pieces of cloth.
Is he correct?

Divisibility by 13

Source: Mayank Bansal (MDB) IIT Delhi ,asked this in headstrong

Problem:

abcabc is a number .Is it divisible by 13?

Absent minded philospher

Source: Some puzzles site

Problem:
One absentminded ancient philosopher forgot to wind up his only clock in
the house. He had no radio, TV, telephone, internet, or any other means
for telling time. So he traveled on foot to his friend’s place few miles down
the straight desert road. He stayed at his friend’s house for the night and
when he came back home, he knew how to set his clock.
How did he know?

A mechanical mind

Source: Initial Problems by Dmitri Fomin

Problem:

Eleven Gears are placed in a plane arranged in a chain.
Can all of them rotate simultaneously?

Average Salary

Source: Delightful Puzzles by Gurmeet ,Similar problems are there in many other forms and different statements

Problem:

Four honest and hard-working computer engineers are sipping coffee at
CCD. They wish to compute their average salary. However, nobody is willing
to reveal an iota of information about his/her own salary to anybody else.
How do they do it?

Probability

Problem:
Santa and Banta are a married couple(don’t know who is he and who is she),
They have two kids, one of them is a girl. Assuming, the probability of each
Gender is ½ . What is the probability that other child is also a girl ?

Answer is not 0.5 if you are thinking.

Murder

Source: www.Brainden.com

Problem:

A donkey behind a donkey,
I am behind that second donkey,
but there is Whole nation behind me.
Its a Murder

Greek Philosphers

Source: The Moscow Puzzles

Problem:
Three ancient Greek philosophers were taking a nap under a tree, a prankster
Smeared their faces with charcoal. When they got up , each of them started
Laughing ,each thinking other two are laughing at each other.
Suddenly one of them stopped laughing.
How did he realized his face is also smeared?

Circles

Source: Mathematical Circles -Dmitri Fomin
Problem:
A Teacher drew several circles on a sheet of paper and asked one of his
students , how many circles are there?
Student replied “Six”. Teacher said “Correct”.
Then he asked the same question to some other student, he replied “seven”.
“That’s right” was the teacher’s reply.
How is this possible?

The mystery of Sphinx

Source: Google

This is a very old Greek puzzle and can be googled easily, but worth sharing.

Problem:

In Greek mythology, the sphinx sat outside the Thebes and asked all the

travelers a question, if they didn’t answered it correctly, The Sphinx used

to kill them. And if answered correctly, the Sphinx will destroy itself.


The riddle: What goes on four legs in the morning, on two legs at noon

And on three legs in the evening.

Oedipus solved the riddle and sphinx destroyed itself.

The legitimate relation

Source: Mathematical Circles-Dmitri Fomin

Problem:
The son of professor’s father is talking to the father of professor’s son
and the professor does not takes part in the conversation. How

Laughing Dog

Source:Mathematical Circles -Dmitri Fomin

Problem:

My dog always laughs before it rains. He laughed today.
”This means it will rain” I thought.
Am I right?

Turtles

Source: Mathematical Circles: Russian Experience by Dmitri Fomin

Problems :Three turtles are walking in the same direction in a row .
First turtle said: there are 2 turtles behind me and no turtle in front of me.
Second said : there is one turtle behind me and one in front of me.
But the last turtle said there are 2 turtles in front of me and two behind as well.
How??

The common elevator puzzle

Source: Some puzzle Site

Problem:

A man works on the 10th floor and always takes the elevator down to the
ground level at the end of the day.
Yet every morning he only takes the elevator to the 7th floor and walks up
the stairs to the 10th floor, even when he is in a hurry. Why?

Planes and Plans

Three sparrows fly outward from a point at the speed of 3 m/s.
Speed of the wind is 4 m/s .After how much time, all of them will be on
the same plane in space ?

Million Dollar Baby

Source: TV show  "Who wants to be a billionaire"

Problem:
Which is worth more: one pound of $ 1 gold coins or half a pound of $ 2 gold coins??

Them Apples!

Source: Some puzzle site.

Problem:

There are Five apples in a basket. Divide them among five girls, so that each of them gets one Apple and there is one apple left in the basket.

A famous one: The Missing Dollar

Source: Asked by Jain in Accenture.

Problem: So here is the problem , quite famous one.

Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

Its a financial paradox.

http://en.wikipedia.org/wiki/Missing_dollar_riddle

Twist

Source : Asked by a fellow in Headstrong

Problem: Why I like Ulan Bator?