Lazy Vera

Source: 300 Moscow Puzzles

Problem: Mother asked Vera to type a manuscript for her. Vera said she will type
20 pages a day. Vera was lazy during the first half of the manuscript and
typed at speed of 10 pages per day and the latter half of the script at 30
pages per day.

Vera said, see I made it on time half of 30 + 10 is 20 which is my average.
Mother said ‘No, You didn’t’.
Who was right and why?

Dollar notes

Source: Bhupesh Bhargava,Algo Embedded systems

Problem: Distribute 127 one rupee notes among 7 wallets So that any integer sum
 from 1 to 127 can be paid without opening the wallets.

Twins

Source: Some Problem website

Problem:   Julius and Vincent are brothers. "We are born within the same hour," says Julius, "on the same day of the same year." "But," says Vincent, "we are no twins!"

How??

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?

Series

Source: Quant company written test

Problem:

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

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.

Twist

Source : Asked by a fellow Headstrong

Problem: Why I like Ulan Bator?

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?

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?

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

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 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

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 ?