You are given a set of balance scales, which you are to use to measure eight
balls. Seven of these balls have the same weight: the eighth ball is heavier
than the rest. What is the minimum number of weighs you could perform to find
the heaviest of the eight balls? Same as above but with 12 balls?

To qualify for a race, you need to average 60 mph driving two laps around a 1
mile long track. You have some sort of engine difficulty the first lap so that
you only average 30 mph during that lap; how fast do you have to drive the
second lap to average 60 for both of them?

A river is flowing downstream at 15 mph relative to the shore. A rowing team is
practicing rowing and at first they row upstream (against the current). They can
only go 1.5 mph relative to the shore at this rate. The guy at the back end of
the boat is wearing a hat when they begin, but after a while his hat falls into
the water (and floats) and it is 15 minutes before they notice it. They then
instantaneously reverse direction and row back to catch up with the hat, rowing
with the same strength or power they were rowing with before. How long will it
take them to catch up with the hat as it is pushed downstream by the current? 

There are 10 open boxes containing 100 coins each. In 9 of these boxes the coins
are made of gold, and in the other the coins are made of copper. You are given
a large digital balance which can be used once only. Can you identify the box
containing copper coins knowing the weight of both gold and copper coins? 

A bag contains a total of n balls with either blue or red color. If five balls
are randomly chosen from the bag, the probability is precisely 1/2 that all five
balls are blue. What's the smallest value of n for which this is possible?
(Hint: Use different number of blue/red balls to get to the answer?)

You are given 5 bags containing 100 coins each. The bags can contain coins of 3
different types that look identical. The first type weighs 9 grams, the second
type 10 and the third type 11 grams. Each bag contains coins of equal weight but
you do not know how many of the 5 bags are of the different types (i.e. all 5
bags might well contain 9 gram coins as far as you are concerned). You are given
a huge digital balance. How many times do you need to use the balance to clearly
determine the type of coin contained in each bag?

You are playing Russian roulette with a six chamber revolver, you load 2 bullets
into the revolver in adjacent chambers. You spin the barrel place the gun to
your head and pull the trigger, you don't shoot yourself. You now have the
option of either spinning the barrel or pulling the trigger again, which do you
take? 

You are in a boat on a lake, in the boat there is a suitcase, you throw this
suitcase over the side of the boat. What happens to the level of the water in
the lake? Does it rise, fall or stay the same?   

You are gambling on the roll of a fair six sided dice, in this game if you roll
a 1 you get $1, if you roll a 2 you get $2, if you roll a 3 you get $3 and so
on. What is the expected return after 100 roles of the dice. (Note: there are a
large number of variations on this game, you should spend some time looking at
various dice games and probabilities) 

You get the number of dollars as the number of dots on the up face of a dice. If
you are not satisfied with the outcome, you can choose to have a second round
of the game and get the number of dollars according to what you got on 2nd
round. If you are still not satisfied, you can proceed to the 3rd round. For
such a game with 2 options, how much you should charge the gamblers to enter the
game?

You have a stick of length 1, then break it up into 3 pieces. What is the 
probability that you can make a triangle with the three pieces.

Solve x in the equation (((x^x)^x)^...) = 2.

Solve the ODE x' = 4-2x with boundary condition x(0) = 1.

Solve the integral{x=0,2}{xf''(x)}dx from 0 to 2 given f(0), f(2), f'(0),
and f'(2).

If the pdf f(x) and cdf F(x) are known, solve E{F(x)}.

I have 6 coins, 3 with double heads, 1 with double tails, 2 are normal with 
a head and a tail. If you pick one coin and flip it 10 times and get all heads,
what is the probability that the coin is with double Heads.

Given an array A(n). write pseudocode to compute y = A(1)x+A(2)x^2+A(3)x^3+....
+A(n)x^(n-1) that will minimize the number of multiplications.

What is the largest positive integer that cannot be written as 42a + b, where a
and b are positive integers and b is composite?

There are 100 tigers and 1 sheep on a island only has grass. Tigers can eat
grass, but they would rather choose to eat sheep. Two conditions:

each time only one tiger eats one sheep, and itself becomes a sheep.
the tigers are smart and can think logically.

Will all the sheeps be eaten finally?

Given a choclate bar with m rows and n columns. If you can break one piece at a
time, then ask what is the least number of times to break it into mn small
pieces.

You want to find the length of a train. Suppose you get on the train at a random
cart and start walking towards a random direction. After you walked 5 carts, you
reached the end of train. What is the most likely length of the train?

Two people play a game. In turn, each player says a number between 1 and 10
(inclusive). The accumulative score is recorded. The aim of the game is force
your opponent to make the total equal to or above 60. As the player going first,
what strategy should you adopt to enable you to guarantee a victory?

You are provided 2 unequal lengths of rope and told that both take exactly 1
hour to burn from end to end, although they don't necessarily do so in a uniform
fashion. How would you go about measuring an exact 15 minute period?

A line of unit length is cut into 3 pieces. What is the expected length of the
longest piece?

Let's flip a coin. I start from $5. If the coin shows a head, I get $1; if it's
a tail, I lose $1. The game ends when I lose all my money or I reach $10. What
is the probability that I end up with $10? What is the expected number of flips
until the game stop?

In a room stand n armed people. At each chime of a clock, everyone
simultaneously spins around and shoots a random other person. The persons shot
fall dead and the survivors spin and shoot again at the next chime. Eventually
there is one or none survivor. As n grows, what's the limiting probability that
there will be a survivor?

How many dots can you put on a ball so that all dots have the same (sphere)
distance to each other?

You have some integers between 1-1000. You want to find the numbers that are not
part of this group, but also in 1-1000. Find the linear time algorithm with
constant memory space.

In a room there are many people, some of them wear red hats. They can only see
the others but not himself/herself. If you open the door of the room and ask
the people wearing red hats to go out of the room, the first 5 times nobody went
out, but on the sixth time, some people went out. How many people went out?

There are two doors: one is entrance to heaven, another entrance to hell. Also,
one door is guarded by an angel who only tells truth, another door is guarded
by an angel who only tells false. If you are allowed to ask one of the angels a
question, who and what will you ask if you want to go to heaven.

Given a deck of 52 cards. If you flip the cards one at a time and the nth card
flipped up is the first ace, what is the expected value of n?

A two-pan balance and 16 coins of different weights are given. What is the
fewest number of usages of the balance needed to determine the heaviest coin,
the second heaviest coin, and the third heaviest coin?