... try
these riddles!
Do you have a riddle? If so, send it along
with the source and the solution to me at mcarlton@calpoly.edu.
You are a contestant on the game show Let's Make a Deal, and emcee Monty Hall has a game for you to play. On stage are three huge doors, and he informs you that hidden behind one of the three doors is a brand new sports car, behind another is a donkey, and behind another is 400 pounds of bananas. (This may seem obvious, but your goal is to get the car, not the donkey or the bananas.) He asks you to choose one door, and you will win the prize behind that door. You choose, but before he reveals what you have won, Monty reveals what's behind one of the doors you did not pick, and it's not the car. Before revealing what lies behind the remaining two doors, he makes you one final offer: if you wish, you may switch from your choice to the other remaining door. The question is: Should you switch, should you not switch, or does it matter?
A professor tells her assistant that she dined with three people last night. She also tells him that the sum of the three people's ages is twice the secretary's own age and that the product of the three people's ages is 2,450. Then, she asks him to tell her the ages of the three people. After a while, the assistant tells the professor that he doesn't have enough information to solve the problem. She agrees and adds that she is older than all three people with whom she dined. The assistant, who knows her age, promptly gives the professor the correct ages. The question is: What are the ages of all five people in this story?
You stand at a fork in the
road. Next to each of the two forks, there stands a guard. You know the
following things: 1. One path leads to Paradise, the other to Death. From
where you stand, you cannot distinguish between the two paths. Worse, once
you start down a path, you cannot turn back. 2. One of the two guards always
tells the truth. The other guard always lies. Unfortunately, it is impossible
for you to distinguish between the two guards.
You have permission to ask
one guard one question to ascertain which path leads to Paradise. Remember
that you do not know which guard you're asking -- the truth-teller or the
liar -- and that this single question determines whether you live or die.
The question is: What one question asked of one guard guarantees that you
are led onto the path to Paradise, regardless of which guard you happen
to ask?
You have undoubtedly heard
of those mysterious islands where half the inhabitants always tell the
truth and the other half always lie. Nobody seems to have actually visited
one of these islands, but everyone knows of someone who has, someone who
found himself at the fork in a road with a strange islander (who could
be either a truth teller or a liar) and who was able to ask only one question
to find the right path.
That's simple. So is the
case where the islanders don't speak English and you have to interpret
their response. It's even possible to find the right road if half of them
are zombies or psycho killers and you are armed with one silly question.
I once found myself on an
island that made those places look like "Romper Room." Picture, if you
will, the Isle of Row, a one-acre forsaken swatch of desert in the middle
of the Sea of Troubles. Despite its diminutive size, Row has no less than
four kinds of people, all outwardly indistinguishable from one another.
There are the members of the First Family, who always tell the truth, and
the Pretenders, who never do. There are the Eccentrics, who may or may
not tell the truth, depending on whim. Finally there are the Wimps, who
are incapable of speaking unless they have heard one of the other kinds
of people speak, and then they obsequiously chime in.
One day, as luck would have
it, I found myself at the only crossroads on the island, facing four possible
routes. Three Rowians stood by, milling about, and I had only two questions
to ask in order to reach, as directly as possible, the fabled 100-foot
Tower of Schmooze, the island's premier, albeit only, tourist attraction.
What did I do?
Yours in pursuit of truth,
Dr. Crypton.
You have twelve coins, eleven identical and one different. You do not know whether the "odd" coin is lighter or heavier than the others. Someone gives you a balance and three chances to use it. The question is: How can you make just three weighings on the balance and find out not only which coin is the "odd" coin, but also whether it's heavier or lighter?
Solution
Gordon Marquardt (Milwaukee,
WI) created the following solution algorithm. Check
it out!
A family has newly moved into the area. A neighbor asks the parents how old their three girls are. The father answers that the product of their ages is 36 and, pointing to his car, adds that the sum of their ages equals the first two digits in his license plate number. After a short struggle with pen and paper the neighbor says he needs more information. He is then told that the oldest daughter loves strawberry ice cream. "Oh, now I understand," says the neighbor, who promptly comes up with the right answer. What are the ages of the three children?
"What's your phone
number, Drew?" asked Eliot.
"Well," said Drew, "if
you replace the first digit of your phone number with the next lowest odd digit,
you get my number."
"And the code?"
"Curiously," said Drew, "the product of the four digits in that
number is the same as the square root of my phone number."
"But that's insufficient information," pointed out Eliot.
"Yes," said Drew. "But if, in addition to that information, I
were to tell you the sum of those four digits, then you'd have enough."
What is Drew's code? Note: In Britain, the "code" is four
digits.
Suppose you're taking a multiple-choice quiz. One question has three choices. Not knowing the answer, you randomly guess A. The instructor then announces that C is incorrect. Should you switch to B before turning in your paper?
9. The Bachelor King (thanks to Mike Groat at Computer Sciences Corporation)
An old king is about to die and he has no offspring to inherit the crown. So he summons the three wisest men from his kingdom and puts them to a test. He tells them that he is about to put them in a room and have his aide put a hat on each of them. Each hat may or may not have a dot on it, but at least one hat will have a dot. They may not touch the hats, nor communicate in any way. The first one that correctly identifies whether his hat has a dot will become the next king. If he is wrong, or if he breaks the rules, he will be killed. Then he sends all three wise men into the room.
The king then tells his aide to put dotted hats on all three.
A few minutes later one of the wise men returns and announces proudly that he has a dot. How did he know?
10. The Drunken Warden (thanks to Mike Todd)
A jail consists of 100
cells in a line, all starting out closed. The warden gets drunk one night and
goes along opening every single cell. He then returns to the beginning, and
"toggles" every second cell -- in this case, they're all open, so
he closes every other cell door. He then runs to the beginning again, and "toggles"
every third cell, then again with every fourth cell, and so on until the very
last run in which he only toggles the hundredth cell, then drops down from exhaustion.
How many cells are left open after this process?
11. Coins in the Dark (thanks to Ilsa Marie Dohmen)
There are 100 coins scattered in a dark room. 90 have heads facing up and 10 have tails up. You cannot distinguish (by feel, etc.) which coins are which. How do you sort the coins into two piles that contain the same number of tails?
