1.  I have 12 balls.  One of which is heavier or lighter than the other 11
balls.  I will also give you strict balance i.e. it will only display
whether two weights are equal, the left side is heavier, or the right side
is heavier.  I will allow you three uses of the balance and after the
third use I would like you to be able to tell me which ball is heavier or
lighter and if it is heavier or lighter than the rest.  

2.  Suppose there exist a nation consisting exclusively of 10 million
married couples.  There also does not exist any children or any other such
person in the nation except for the couples.  Every male in this country
knows to whom ever other male is married to.  So that given any woman of
the nation, every male knows to whom she is married.  There is also I
harsh law in this nation.  If a male has proof that his wife is cheating,
he must execute her on the following day.  There is no choice in this
manner and all husbands would like their wives killed if they knew they
were cheating.  (yes this is quite confusing to set up)  
    Now each husband knows if every other wife is cheating except his own.
All men of the nation have this ability except for the king, who has
knowledge of all wives including his own.  
    On day zero the king announces to the country that there is infidelity
in the nation i.e. that there is adultery among the citizens.  On day one
no one dies.  On day two no one dies.  On day three no one dies.  On day
four people die.  My question is how many people die on day four and how
do you know?

3)  Which offer is better and why?

A's offer:  You are to make a statement.  If the statement is true, you get
exactly ten dollars.  If the statement is false, then you get either less 
than or more than ten dollars but not exaclty ten dollars.

B's offer:  Your are to make a statement.  Regardless of whether the statement
is true or false, you get more than ten dollars.

These are from Robert Samal

4) You have two ropes and a box of matches. If you light any of the
ropes, it will burn exactly one hour. However it can burn very unevenly
(like first half in ten minutes, the other one in the remaining
fifty minutes, ...). Can you measure 45 minutes with these two ropes?

5) Forty bandits are sentenced to death. However they have a way to 
save themselves. Before the execution they will be seated in a row
(so that everybody sees all bandits before himself) and everybody
gets a hat on his head, the hat is either black or white, but you don't
know the color of your hat. Now they are asked to say in turns what color
has their hat, starting from the bandit seating in the back.
If you tell the right color, you are free, if not, you will be
executed.  How many of the bandits can be saved, provided they can decide
on a strategy before the whole process starts?

These are from Daniel Kral

6) There are 26 phone cables in an elevator pit in a 100-floor skyscraper.
   Their ends are signed by letters 'A' through 'Z' in the basement and 
   by numbers '1' to '26' in the last (100st) floor. Unfortunately, 
   you don't know how the ends are matched. You have got a battery,
   a bulb and some short wires. You're in the basement now and
   the elevator is out of order. Your task is to find out the matching
   of the cable ends. It is possible to find the matching by going only
   once up and once down.
7) You are in a desert and you have got a camel and 3000 bananas.
   You want to move as many as possible bananas to an oasis 1000 miles far.
   There are two problems - a camel can carry only 1000 bananas and
   it eats a banana each mile. (If it did not ate, it would die.)
   How many babanas can you move to the oasis? (The bananas in the camel's
   maw are not counted.)

8) Consider three exactly same airplanes; the size of a tank of any of them
   allows the plane to fly for exactly half the way around the world.
   The planes are capable to move fuel between their tanks during the flight.
   All the planes move with same speed (i.e. none of them can fly slower or
   faster than the other ones). Find out the plan how one of them can
   fly around the world without landing. The planes can land only
   at the original airport where all of them are now.
9) Imagine the following: You have a shawl around your head in such a way
   that you cannot see anything. In front of you there is a square table
   with four cups, each of them is located in one of its corners. The cups are
   positioned with the bottom either up or down. You are able to determine 
   their positions by your hands. The rules are as follows: You choose two 
   corners (near left, near right, rear left, rear right), you determine 
   the positions of the cups in these two corners and you can change 
   the position. Then the table moves around its center several 
   times (e.g. 5.25 times, 3.5 times, 6 times etc.). You are not able to 
   determine the number of its rotations. Now you can choose next two corners,
   determine the positions, change them and the table moves again etc. 
   You should find out what to do in order the cups to be all with bottoms 
   down (after fixed finite number of rotations).