Fixed point theorem

Source: Nash Equilibrium's derivative also, in Martin's Gardener My best Mathematical and Logical Puzzles


Problem:  One morning at 6 am, a monk began climbing a tall mountain, which happened to only have one path to the top. He ascended the path at his leisure, taking some stops along the way. He reached the top at 8 pm.

The next morning at 6 am, the monk descended the mountain along the same path. He took several breaks along the way, and reached the bottom at 8 pm.

The amazing result: there is some spot on the path that the monk occupied at precisely the same time of day for both trips. Why is this?

This is true even if the monk took breaks to meditate, chatted it up with a fellow traveler, or if he took some time to massage his feet. You get the point: it really does not matter what he did during the trips going up or down.

Birthday problem or a paradox

Source: wikipedia

Problem: There is a big line of people waiting outside a theater for buying tickets. The theater owner comes out and announces that the first person to have a birthday same as someone standing before him in the line gets a free ticket. Where will you stand to maximize your chance.

Bertrand's paradox

Source: Internet

Problem:  In a village, the barber shaves everyone who does not
shave himself/herself, but no one else.
Who shaves the barber?

It’s called Bertrand’s paradox after Bertrand Russell.

Sleeping Beauty Paradox

Source: Tim Whitter's Paradoxical natures

Problem:  Its sleeping beauty paradox, quite famous.
I have not fathomed it out yet.

The paradox imagines that Sleeping Beauty volunteers to undergo the
 following experiment. On Sunday she is given a drug that sends her to sleep.
 A fair coin is then tossed just once in the course of the experiment to
determine which experimental procedure is undertaken. If the coin comes up
 heads, Beauty is awakened and interviewed on Monday, and then the
 experiment ends. If the coin comes up tails, she is awakened and interviewed
 on Monday, given a second dose of the sleeping drug, and awakened and
interviewed again on Tuesday. The experiment then ends on Tuesday,
 without flipping the coin again. The sleeping drug induces a mild amnesia,
so that she cannot remember any previous awakenings during the course of
the experiment (if any). During the experiment, she has no access to anything
 that would give a clue as to the day of the week. However, she knows all the details of the experiment.
Each interview consists of one question, "What is your credence now for the proposition that our coin landed heads?"

This problem is considered paradoxical because the answer is often given as either 1/3 or 1/2.

Think!! :)

Monty Hall Problem

Source: Various(Movies e.g. 21, Maths courses, books on basic probability)

Problem: Its Monty hall, also used in movie ‘21’,when Kevin spacey asks
Jim Sturgess in form of game show host problem.


You are on a game show and there are three doors. The presenter tells
 you that behind one of doors there is a car and behind the other two are
 goats. If you pick the car you win it. After you have picked a door the
 presenter opens a different door with a goat behind it, he then gives you
the chance to change your choice to what door you open. What should you do?

Lexicon

Source: Moscow Puzzles

Problem:

A slim crocodile living in the Nile took a child. His mother begged to have

 him back. The crocodile could not only talk, but was also a great sophist

and stated, "If you guess correctly what I will do with him, I will return

 him. However, if you don't predict his fate correctly, I'll eat him."

What statement should the mother make to save her child?

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?

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?

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

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 ?