1.1. Among 12 coins find the false one, using scale only 3 times. However you don't know if the false coin is heavier then others, or easier.
Medium
level
2.1. Use numbers 2,4,6,8 with any of four mathematical operations to get 25 !
2.2. A man walks into a bar, orders a drink, and starts chatting with
the bartender. After a while, he learns that the bartender has three
children. "How old are your children?" he asks. "Well," replies
the bartender, "the product of their ages is 72." The man thinks
for a moment and then says, "that's not enough information." "All
right," continues the bartender, "if you go outside and look at the building
number posted over the door to the bar, you'll see the sum of the ages."
The man steps outside, and after a few moments he reenters and declares,
"Still not enough!" The bartender smiles and says, "My youngest plays
the violin."
The Question: How old are the children?
2.3. You are a participant in a quiz. The quiz master shows you three
closed doors. He tells you that behind one of these doors there is a prize,
and behind the other two doors there's nothing. You select one of the doors,
but before you open it the quiz master contiously picks out a remaining
empty door and shows that there is nothing behind it. The quiz master offers
you a chance to switch doors with the remaining closed door.
The Question: Should you stick to your choice?
Easy
level
3.1. Once there were three Doctorates of Logic (i.e. they could trust
each
others reasoning powers explicitly) who were on a safari in the wilds
of
Africa at a time when there were dangerous and conniving tribes of
cannibals. Through misfortune they were captured and were standing
in
front of the boiling pot, when they noticed the chief's daughter playing
with 5 kittens, 2 black and 3 white. Instantly, they saw a chance to
freedom. Through some mysterious means of communication, they indicated
that they were gods and should not be harmed. To prove it they challenged
the chief to blindfold them, sit them in a circle put one of the kittens
behind each and hide the other two. Further, they were to be arranged
so
that when unblindfolded, each might see the two kittens behind the
others, but not the one behind himself. One at a time their blind folds
should be taken off and if, by the third man, one had not named the
color
of the kitten behind him, or any named it wrong, then they were false
gods, worthy of death.
Thus, the challenge began. When the first man was unblindfolded,
he took
one quick look and indicated that he could not be sure. Then the second
man was unblindfolded and after a prolonged look he announced with
cool
calmness that neither could he be certain. There was restlessness among
the natives who began to murmur that perhaps it would be too easy for
the
third "guesser". In fear that he might not make a strong enough
impression of their powers, the third man named the color of the kitten
behind before they could unblindfold him, and thus, the natives in
great
awe released them.
Questions for the listener:
1) What was the color of the kitten behind the third man?
2) Would you be willing to bet your life on your answer to the first
question?
3) If "Yes" to the second question, then it is a simple matter to answer:
What were the odds of their gamble?
4.2. There are a carrot, a pile of pebbles, and a pipe lying together
in the middle of a field.
4.2. They're the remains of a melted snowman.