Traps (a.k.a. Brain Teasers)
150. FOUR-DIGIT NUMBER
What is the four-digit number, no zeroes, in which the first number is five
times the last, the second is four more than the first and three times the
third, and the third is two more than the last and two less than the first?
Solution
149. FRENCH SNACK
Pierre stopped at his favorite wine shop to buy a bottle of Sauternes for
the Bastille Day celebration. He spent half of what he had plus $2.00 for
a very special bottle of Chateau d'Yquem. Then he spent half of what he
had plus $3.00 for a small tin of foie gras. Then he stopped at his
favorite bakery and bought brioches to spread the foie gras on, and spent
half of what he had left, plus $4.00. At that point, he had $2.00 left,
with which he bought a small bottle of digestive medicine, just in case.
How much did he have to begin with?
Solution
148. PALINDROMES
A palindrome (like "Madam I'm Adam") can be words, phrases, or even
whole sentences that read the same forward and backward.
See how many of the following palindromes you can work out.
Legal or illegal ways to obtain something:
_ _ _ _ _ _ _ _ _ _ _
A description of an Eskimo who has fallen out of his boat:
_ _ _ _ _ _ _ _ _
Look at lots of judges on the sports scene:
_ _ _ _ _ _ _ _ _ _ _
The big chiefs are showing grief:
_ _ _ _ _ _ _ _ _
A person who lives in a city in Nevada and tends to be solitary:
_ _ _ _ _ _ _ _ _
Solution
147. MONEY TALKS
"See," said the richest man in the world to his secretary as he bought
up another country, "money talks."
The secretary sighed. "He's right, " she said. (The rest is cryptic--a
simple substitution.)
"13-15-14-5-25 20-1-12-11-19, 2-21-20
20-15 13-5 9-20 19-1-25-19
7-15-15-4-2-25-5."
Solution
146. KING TUT'S BIRTHDATE
King Tut died 120 years after King Eros was born. Their combined
ages, when they died, was 100 years. King Eros died in the year
40 BC. In what year was King Tut born?
Ignore any historical inaccuracies; for the sake of this
problem, let's just say that the data are correct.
Solution
145. THE TENNIS GAME
Four people played a tennis game.
(1) The four people were Winifred, her father, her husband,
and their daughter.
After the game, one of them spoke truthfully about one time during
the game:
(2) "I was directly across the net from the server's daughter.
(3) "My partner (on the same side of the net as I) was directly
across the net from the receiver's father.
(4) "The server was diagonally across the net from the receiver
(of course)."
Who spoke?
Solution
144. THE MATH PROFESSOR
It's not easy having a mathematics professor as a new friend. When she
invites you to her house she says, "All the houses on my side of the
street are numbered consecutively in even numbers. There are six houses
on my side of my block and the sum of their numbers is 9870. You don't
know which block I live on, and it's a long, long street, but I will
tell you that I live in the lowest number on my side of the block.
What's the number? Or are you just going to ring the first even-numbered
doorbell for twenty blocks?
Solution
143. WHO'S OLDEST?
Tom is younger than Rose, but older than Will and Jack, in that order.
Rose is younger than Susie, but older than Jack.
Jack is younger than Jim.
Susie is older than Rose, but younger than Jim.
Jim is older than Tom.
Who is the oldest?
Solution
142. THE LUMBERJACK
Said a feller out felling a tree,
"My age I've divided by three.
The result is a square,
Yet my age, I declare,
Is six times a cube. Glory be!"
How old is the lumberjack?
Solution
141. THE MURDERER IN THE MANSION
The owner of the mansion has been murdered! The visitors to the mansion
were Allen, Bixby, and Crain.
1) The murderer, who was one of the three visitors, arrived at the mansion
later than at least one of the other two visitors.
2) A detective, who was one of the three visitors, arrived at the mansion
earlier than at least one of the other two visitors.
3) The detective arrived at the mansion at midnight.
4) Neither Allen nor Bixby arrived at the mansion after midnight.
5) The earlier arriver of Bixby and Crain was not the detective.
6) The later arriver of Allen and Crain was not the murderer.
Who was the murderer?
Solution
140. FIREWORKS SHOW
There are four seats in a row at a Fourth of July fireworks show. Philip
will sit next to Sally, but not next to Gerald. If Gerald will not sit
next to John, who is sitting next to John?
Solution
139. UNCORK THE JUG
A soldier is stranded in a desert with no water and comes across a
native boy who has a jug half full of water.
The boy says, "You can have the water on three conditions:
1) You do not take the cork out of the jug;
2) you do not make a hole in the cork; and
3) you do not break the jug or put a hole in it in any way.
The soldier then proceeds to drink the water. How?
Solution
138. THE LETTER F
How many times does the letter F appear in the statement below?
FANNY FILINGER WAS OF THE IMPRESSION THAT EIGHTY-SIX
YEARS OF HISTORY SHOW THAT SCIENTIFIC RESEARCH IS OF THE
UTMOST IMPORTANCE IN EVERY CASE OF FUTURE GENERATIONS.
Solution
137. STEVE'S BIRTHDAY
To celebrate Steve's birthday his wife Jan (who is 49) has taken him and
six friends to a health spa for the weekend. The eight of them have
different ages which consist of eight consecutive integers. In the sauna
each has a locker number and these too consist of eight consecutive
integers. For example, Christine's is 125 and Steve's is 130. Sitting
naked in the sauna, they are contemplating their common factors and note
that, for any pair of them, their ages have a common factor greater than
one if and only if their locker numbers do.
How old is Steve?
Solution
136. TOY TRAINS
Ben decides to use a new pattern for building trains. He uses 1 block for
his first train, 3 blocks for the second, and 6 blocks for the third. How
many blocks will he need for the sixth train?
Note: There could be an alternate answer, so you'd better defend yours.
Solution
135. SPRING FLOWERS
How many flowers do I have if all of them are roses except two, all of
them are tulips except two, and all of them are daisies except two?
(And what kind of flowers are they?)
Solution
134. THE SHEIK'S SONS
An Arab sheik tells his two sons to race their camels to a distant city to
see who will inherit his fortune. The one whose camel is slower will win.
The brothers, after wandering aimlessly for days, ask a wise man for advice.
After hearing the advice they jump on the camels and race as fast as they
can to the city. What does the wise man say?
Solution
133. WHAT TIME IS IT?
How many minutes is it before six o'clock if fifty minutes
ago it was four times as many minutes past three o'clock?
Solution
132. BULLDOZERS
An engineer who was up in Alaska working on the oil pipeline, was heard
to say, "At the time I said I could finish this section in a week, I
expected to get two more bulldozers for the job. If they had left me
what machines I had, I'd have been only a day behind schedule. As it is,
they have taken away all my machines but one, and I'll be weeks behind
schedule."
How many weeks behind schedule will this make him?
Solution
131. FIND THE WORD
From the following group of letters, remove twelve letters so the
letters that remain, in order, will spell a familiar word.
T A W F E A L M V I E L L I E A T R T W E O R R S D
Solution
130. EDNA'S CATS
Three people make the following statements about a fourth person,
who loves cats:
No. 1 says: "Edna has at least six cats."
No. 2 says: "Don't be silly. She doesn't have that many."
No. 3 says: "But she owns at least one cat."
If only one statement is true, how many cats does Edna have?
Solution
129. TWO PENCILS
You have two pencils, a good one and a cheap one. The good one
cost $1.00 more than the cheap one. You spent $1.10 for both.
How much did the cheap one cost?
Solution
128. LET THEM EAT CAKE
If a man and a half can eat a cake and a half in a minute and a half,
allowing the same rate, how many men would it take to eat 60 cakes in
30 minutes?
Solution
127. SHIPWRECKED BANANAS
There was a shipwreck at sea and Buck, Lance, and Jack were washed ashore
on a small island. Upon reaching shore they promptly fell asleep from
exhaustion. A short time later, Buck awoke and saw that a box of bananas
had been washed ashore. Buck ate one third of the bananas and went back
to sleep. Lance soon awoke and upon seeing the bananas, ate one third of
what was left and then fell asleep. Jack woke next and assumed the other
two hadn't eaten any bananas, so he ate one third of what remained. When
Jack had finished, there were eight bananas left over. How many bananas
were in the box originally?
Solution
126. APARTMENT DOORS
(This is one of my oldest and favorite traps. - jr)
There are 1000 tenants and 1000 apartments. The first tenant opens all the
doors. The second tenant closes every other door. The third tenant goes to
every third door, opening it if it is closed and closing it if it is open.
The fourth tenant goes to every fourth door, closing it if it is open and
opening it if it is closed. This continues with each tenant until the
1000th tenant closes the 1000th door.
How many doors are open?
Solution
125. WHO KILLED KILRAINE?
Daniel Kilraine was killed on a lonely road, two miles from Pontiac,
Michigan, at 3:30 a.m., March 17, 1952. Otto, Curly, Slim, Mickey, and
the Kid were arrested a week later in Detroit and questioned. Each of
the five made four statements, three of which were true and one of
which was false. One of these persons killed Kilraine. Whodunnit?
Their statements were:
OTTO: I was in Chicago when Kilraine was murdered. I never killed
anyone. The Kid is the guilty one. Mickey and I are pals.
CURLY: I did not kill Kilraine. I never owned a revolver in my life.
The Kid knows me. I was in Detroit the night of March 17.
SLIM: Curly lied when he said he never owned a revolver. The murder
was committed on St. Patrick's Day. Otto was in Chicago at this time.
One of us is guilty.
MICKEY: I did not kill Kilraine. The Kid has never been in Pontiac. I
never saw Otto before. Curly was in Detroit with me on the night of
March 17th.
THE KID: I did not kill Kilraine. I have never been in Pontiac. I
never saw Curly before. Otto erred when he said I am guilty.
Solution
124. THE LONELY GUY
Jed Recluse lived alone and he preferred it that way. Jed never had any
visitors and he never visited anyone. Since Jed never left his house it was
necessary to have his supplies delivered every two weeks. One dark and
stormy night Jed lost control of his senses, turned off all the lights and
went to sleep. The next morning it was discovered that Jed's actions
resulted in the deaths of several people. Why?
Solution
123. A TRASHY TRAP
A man goes to the store and buys a box of 10 plastic garbage bags. He uses
one bag each day to collect and dispose of his trash. On the first day,
the first thing he throws away is an old newspaper. On the second day,
the first thing he throws away is a used tin can. On the third day, the
first thing he throws away is a glass bottle. On the fourth day, the first
thing he throws away is an empty milk jug. On the fifth day, the first
thing he throws away is an old newspaper. What's the first thing he throws
away on the 10th day?
Solution
122. MARILYN
Beginning of time, middle of nowhere, second fiddle, first string,
second lieutenant, last rites, third dimension, end of eternity,
finishing touches, last in line, first class, last supper, first edition,
final judgment, first choice, second coming, first down, end table.
Last straw, second fiddle, first lady, second blessing, end of eternity,
starting over, second guess, second guess, third base, last name,
second lieutenant, end product, second fiddle, first name, end of eternity,
first off, second guess, middle America, first class, starting over,
second class, second guess, third dimension, first name?
Marilyn replied: Okay. But it's no secret anymore!
Explain.
Solution
121. STUDENT COMPETITION
Four students competed in English, French, logic, and math contests
and are wondering about the outcome.
Student No. 1 thinks No. 4 won the logic award.
Student No. 2 thinks No. 3 won the English prize.
Student No. 3 thinks No. 1 did not win the math title.
Student No. 4 thinks No. 2 won the French trophy.
As it turns out, the winners of the English and French contests
were wrong, and the winners of the math and logic contests were right.
Who won which contest?
Solution
120. THE HARDWARE STORE
A man went into a hardware store to purchase something almost everyone
has around the house. He said to the clerk, "How much are these?"
The clerk said, "They're $1 each -- 100 would be $3."
The customer said, "I'll take 87."
The clerk said, "That will be $2."
What did the man purchase?
Solution
119. SUPER BOWL SCORE
I am not much of a football fan; in fact, yesterday's game was the first
one I watched all season. Nevertheless, I found that, as usual, I was
able to accurately predict the score before the game even started. Some
think that I am psychic, others that I posess supernatural powers (all
right, not really, but that's what the card says!).
How is it that I can be accurate about the score over 99 per cent of the
time?
Solution
118. BLASTING TREES
Dynamite is a tool commonly used to cut down trees. To cut a tree 18" in
diameter requires five sticks of dynamite: one on the north, south, east,
and west sides of the tree, and the fifth stick on the side to which the
tree should fall. During construction of a dam, a tree 18" in diameter was
completely covered by water. Since the tree top was fouling the boat's
propellers, it had to be cut down. A diver went down and put a stick of
dynamite on four sides of the tree. Since the current is flowing south at
2 knots per hour, on which side of the tree would you instruct the diver
to put the fifth stick of dynamite if you wanted the tree to fall north.
P.S. Yes, the dynamite will work under water.
Solution
117. FIREMEN'S VACATIONS
Gardner, Plunkett, Maloney, Phelps, and Lopez work for the Littleville
Fire Department. Each gets two weeks of vacation a year. Last year, each
took his first week in the first five months of the year and his second
week in the last five months. If each man took each of his weeks in a
different month from the other men, in which months did each man take his
first and second week?
Here are the facts:
1. Plunkett took his first week before Gardner, who took his before
Phelps; for their second week, the order was reversed.
2. The man who vacationed in March also vacationed in September.
3. Lopez did not take his first week in March or April.
4. Neither Lopez nor the man who took his first week in January took his
second week in August or December.
5. Maloney took his second week before Plunkett but after Lopez.
Solution
116. CHRISTMAS LIGHTS
A forty-foot string of Christmas lights hangs between two buildings,
attached at the same height at both ends. The shape of this string is
called a "catenary." If the distance from the points of suspension to
the lowest point of the string is twenty feet, how far apart are the
buildings?
Solution
115. BOOMERANGS
Say that I have only one boomerang. Originally I had more, but I gave
half of them plus half a boomerang to my little brother. That made him
mad, so I gave him half of what I had left plus half a boomerang more.
How many boomerangs did I start with?
Solution
114. THE PRINCESS OF PUZZLELAND
Our hero, the brave knight, is trying to rescue the beautiful Princess of
Puzzleland. The maiden has slipped him a message. She will be able to
stand at the stable gate from 12:30 to 12:40--but no more than those ten
minutes--on the following day. If he arrives promptly, she will elope
with him. If not, she will be married later that same evening to his hated
rival. The castle is 12 miles away. The first third is uphill, and his
horse can make 4 miles per hour uphill; the second third is level, at 8
miles per hour; and the last part, one-third, is downhill, at 12 miles
per hour. He figures that averages out to 8 miles per hour, so if he
leaves at 10:55 to give himself five minutes' leeway, he should arrive
exactly within the 10 minutes. Of course, he can't get there too early,
or he'll be caught hanging around.
Does he make it in time? Why or why not?
Solution
113. COMING HOME
The family had missed the plane back home and all its members were very
irritated. "Oh well," said the older boy, "if it were six hours later,
we'd only have to wait one-fifth as long until midnight, when the plane
comes, as we'd have to wait if it were two hours earlier now." Figuring
that out helped pass the time. What time was it?
Solution
112. MAKE ANOTHER WORD
There seems to be only one other word that can be made from the letters
in the word IMPORTUNATE. Find it.
Solution
111. CRYPTOGRAM
The following is an easy type of substitution cryptogram (each letter
standing for a different letter--the same substitution each time).
UR UA NYXG RII GIR RI SI
RGWAW RGUBFA EUFGR BIQ
Solution
110. HOW WIDE THE RIVER?
Two boats one on each side of a river leave the dock at the same time
and start across the river. They travel at constant speed, however,
one travels faster than the other. They pass each other 2100 ft. from
the side the slower boat left from. When each boat reaches the other
side, it waits for fifteen minutes and then starts back across the river,
again traveling at constant speed. They pass each other 1300 ft. from
the side of the river that the slower boat just left from. How wide is
the river?
Solution
109. GUPPIES
Out of 200 fish in an aquarium, 99% are guppies. How many guppies must
be removed so that the percentage of guppies remaining in the aquarium
is 98%?
Solution
108. THE JUDGE'S WIFE
A 1 G 7 M 13 S 19 Y 25
B 2 H 8 N 14 T 20 Z 26
C 3 I 9 O 15 U 21
D 4 J 10 P 16 V 22
E 5 K 11 Q 17 W 23
F 6 L 12 R 18 X 24
Edwin is a judge and a numerologist. He is married to a woman whose name:
1) has a "product" that is the same as that for JUDGE; using the
correspondence of letters and numbers above, this product is
10 x 21 x 4 x 7 x 5;
2) has no letter in common with JUDGE;
3) has no third letter of the alphabet because 3 is his unlucky number;
4) has its letters in alphabetical order when the first letter and
the second letter are interchanged.
What is the name of the judge's wife ?
Solution
107. WHO'S ON THE KEYBOARD?
Name a famous person whose name can be typed (using standard touch-typing
positions) in the following manner:
First Name - 5 letters - entirely by the right hand
Last Name - 6 letters - entirely by the left hand (alt.: 7 letters)
Solution
106. FUSSY MARGOT
Margot likes knights, but not battlers; she likes writing but not typing;
she likes to listen but not to sing. Does she like an unknown or a famous
author?
Solution
105. OCCUPATIONS AT A PARTY
Pam, Ray, Sue, and Tom are an archaeologist, a botanist, a chiropractor,
and a dentist--though not necessarily in that order. At a party Tom said
to the botanist that Sue would be along in a minute, the chiropractor
congratulated the dentist on his engagement to Sue, and Pam took a picture
of the chiropractor standing next to Ray. What is the occupation of each
person?
Solution
104. EQUAL PRODUCTS
A D
B G E
C F
Each of seven digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is:
1) Represented by a different letter in the figure above.
2) Positioned in the figure above so that the products ABC, BGE, and DEF are
equal.
Which digit does G represent?
Solution
103. SPELLING NUMBERS
Suppose you spell out the numbers: one, two, three, and so on. What is
the smallest number that contains the letter "a"?
Solution
102. THE TRAINED CHIMPANZEE
A trained chimpanzee has learned a trick whereby he can throw a baseball
so that it travels a short distance, comes to a complete stop, reverses
direction and then returns to him! He doesn't bounce it off another
object or hit it with anything, nor does he tie anything to it. How does
he do it?
Solution
101. FIFTY-FIVE CENTS
I have two coins that add up to 55¢. One of them is not a nickel.
What are the two coins?
Solution