Interesting puzzles
Puzzle 1
The Beatles have to be at a concert across the river in 17 minutes. The
problem is that the bridge across the river is very weak and is strong
enough to hold only two people at a time (only two people can cross at a time).
They have only one flashlight and anybody crossing the river must have the
flashlight at all times.
John can cross the bridge in 1 minute, Paul needs 2 minutes, George needs 5
minutes and Ringo needs 10. Can they make it to the concert in time?
If so, how?
Puzzle 2
There is a town of monks. All of the monks have either brown or blue eyes.
There are no reflective surfaces in the town and the monks have a vow of
silence, so no monk knows what color his eyes are. Every morning the monks
eat breakfast around a large round table where they can see everyone else's
eyes.
One day, the head monk makes a decree that all blue eyed monks must
leave. Nothing happens until the morning of the 21st day, when at
breakfast all the blue eyed monks are gone. What happened?
Puzzle 3: 100 prisoners in solitary cells
There's a central living room with one light bulb; the bulb is initially off.
No prisoner can see the light bulb from his or her own cell. Everyday, the
warden picks a prisoner equally at random, and that prisoner goes to the
central living room. While there, the prisoner can toggle the bulb if he
or she wishes. Also, the prisoner has the option of asserting the claim that
all 100 prisoners have been to the living room. If this assertion is false
(that is, some prisoners still haven't been to the living room), all 100
prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity. The prisoners are allowed to get together one night in the courtyard, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?
Puzzle 4: Dog in the circle
A man, initially placed at the center of a circle, wants to escape from the
circle. Unfortunately, the circle is guarded by a vicious dog, who would eat
the man. Fortunately, the dog is constrained to stay on the periphery of the
circle. The dog can run upto 4 times the speed of the man, and change
direction instantaneously at any time.
Can the man escape from the circle? If so, how?
Puzzle 5:
You are a prisoner in a foreign land. Your fate will be determined by a
little game. There are two jars, one with 50 white marbles, and the other
with 50 black marbles. At this point, you are allowed to redistribute the
marbles however you wish: the only requirement is that after you are done
with the redistribution, every marble must be in one of the two jars.
Afterwards, both jars will be shaken up, and you will be blindfolded and
presented with one of the jars at random. Then you pick one marble out of
the jar given to you. If the marble you pull out is white, you live;
if black, you die.
How should you redistribute the marbles to maximize the probability that
you live. What is this maximum probability (roughly)?
Puzzle 6:
Three coworkers would like to know their average salary. However, they are
self-conscious and don't want to tell each other their own salaries, for fear
of either being ridiculed or getting their houses robbed. How can they find
their average salary, without disclosing their own salaries?
Puzzle 7:
The FBI has surrounded the headquarters of the Convex corporation. There are
n people in the building, each either an engineer or a manager. All computer
files have been deleted, and all documents have been shredded by the managers.
The problem facing the FBI is to separate engineers from managers, so that all
the managers can be locked up and all the engineers can be freed. Each of the
n people knows the status of all the others. The interrogation consists
entirely of asking person i if person j is an engineer or a manager. The
engineers always tell the truth. What makes it hard is that the managers may
not tell the truth. In fact, the managers are evil geniuses who are conspiring
to confuse the interrogators.
Under the assumption that more than half of the people are engineers, can
you suggest a strategy for the FBI to find one engineer with at most
n-1 questions?
Is this possible in any number of questions if half the people are managers?
Puzzle 8:
You have 20 blue balls and 14 red balls in a bag. you put your hand in and
remove 2 at a time. if they're of the same color, you add a blue ball to the
bag. if they're of different colors, you add a red ball to the bag. (assume you
have a big supply of blue & red balls for this purpose. note: when you take the two balls out, you don't put them back in, so the number of balls in the bag keeps decreasing). what will be the color of the last ball left in the bag?