Chameleons

Source: Some Maths Blog

Problem: On an island live 13 purple, 15 yellow and 17 maroon chameleons. When two chameleons of different colors meet, they both change into the third color. Is there a sequence of pairwise meetings after which all chameleons have the same color?

Insect in 3D

Problem: An ant crawls from one corner of a room to the diametrically opposite corner
 along the shortest possible path. If the dimensions of the room are
 3 x 4 x 5, what distance does the ant cover?

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?

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?