It's fun to solve brain teasers and I've heard your brain is like a muscle. If you exercise it (by teasing it) you'll have a fit brain. Even if that's not true, I still like to solve them.
If you know some good brain teasers, please send them to me. It can also be useful to know how to solve these for job interviews. For some reason interviewers think if you know how to solve puzzles and can think quickly you'll be an ideal employee. Have fun :)
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You have a fox, a chicken and a sack of grain. You must cross a
river with only one of them at a time. If you leave the fox with the
chicken he will eat it; if you leave the chicken with the grain he will
eat it. How can you get all three across safely?
Take the chicken over first. Go back and bring the grain next, but
instead of leaving the chicken with the grain, come back with the chicken.
Leave the chicken on the first side and take the fox with you. Leave it
on the other side with the grain. Finally, go back over and get the
chicken and bring it over.
You have 12 black socks and 12 white socks mixed up in a drawer.
You're up very early and it's too dark to tell them apart.
What's the smallest number of socks you need to take out (blindly) to be sure of having a matching pair?
3 socks. If the first sock is black, the second one could be black,
in which case you have a matching pair. If the second sock is white,
the third sock will be either black and match the first sock, or white
and match the second sock.
What is special about the following sequence of numbers?
8 5 4 9 1 7 6 10 3 2 0
The numbers are in alphabetical order.
(eight, five, four, nine, one, seven, six, ten, three, two, zero)
Three travelers register at a hotel and are told that their rooms
will cost $10 each so they pay $30. Later the clerk realizes that
he made a mistake and should have only charged them $25. He gives
a bellboy $5 to return to them but the bellboy is dishonest and
gives them each only $1, keeping $2 for himself. So the men actually
spent $27 and the bellboy kept $2. What happened to the other
dollar of the original $30?
There is no missing dollar from the original $30 because after getting $1 back, the three travelers had paid a total of $27 for their room ($9 each), not $30. Out of that $27, the hotel has $25 and the clerk kept the remaining $2. If you still want to work from the original $30, the travelers have $3, the hotel has $25 and the bellboy has $2. The misleading part is adding the bellboy's $2 to the $27, when in fact it should be subtracted.
You are the bus driver. At your first stop, you pick up 29
people. On your second stop, 18 of those 29 people get off, and at the
same time 10 new passengers arrive. At your next stop, 3 of those 10
passengers get off, and 13 new passengers come on. On your fourth stop
4 of the remaining 10 passengers get off, 6 of those new 13 passengers
get off as well, then 17 new passengers get on. What is the color of
the bus driver's eyes?
U2 has a concert that starts in 17 minutes and they must
all cross a bridge to get there. All four men begin on the
same side of the bridge. You must help them across to the
other side. It is night. There is one flashlight. A
maximum of two people can cross at one time. Any party who
crosses, either 1 or 2 people, must have the flashlight with
them.
The flashlight must be walked back and forth. It cannot be
thrown and other tricks like that are not needed to solve the problem.
The solution is simply a matter of allocating resources in a certain
order. Each band member walks at a different speed.
A pair must walk together at the rate of the slower man's pace:
Bono: 1 minute to cross
Edge: 2 minutes to cross
Adam: 5 minutes to cross
Larry: 10 minutes to cross
For example: if Bono and Larry walk across first, 10 minutes
have elapsed when they get to the other side of the bridge.
If Larry then returns with the flashlight, a total of 20
minutes have passed and you have failed the mission.
You get to figure this one out on your own.
If you're having a hard time, here's a hint:
There is a valid answer that doesn't require
tricks like throwing the flashlight or shining it backwards or having
some other means of moving the flashlight.
There's an assumption people often make that keeps you from solving this.
Two members cross the bridge each time, but neither one of the two
the crossed need to return. Think about how that would be possible.
If you're still stuck, use objects to simulate their movement.
Use whatever you have laying around - pens, paper, erasers - and move
them back and forth. Good luck!
Why is it very common to have a 9 minute snooze interval on alarm
clocks, why not 10 instead?
By setting the snooze time to 9 minutes, the alarm clock only needs to
watch the last digit of the time. So, if you hit snooze at 6.45, the
alarm goes off again when the last digit equals 4. They couldn't make it
10 minutes, otherwise the alarm would go off right away, or it would take
more circuitry.
A bookworm eats from the first page of an encyclopedia to the last
page in a straight line. The encyclopedia consists
of ten 1000-page volumes and is sitting on a bookshelf in the usual
order. Not counting covers, title pages, etc., how many pages does the
bookworm eat through?
On a book shelf the first page of the first volume is on the "inside",
so the bookworm eats only through the cover of the first volume, then
8 times 1000 pages of Volumes 2 - 9, then through the cover to the 1st
page of Vol 10 for a total of 8,000 pages.
Note: The question asks how many pages, not how many sheets of paper.
An Arab sheikh 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 advise. 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?
An 18-wheeler is crossing a 4 kilometer bridge that can only
support 10,000 kilograms and that's exactly how much the rig weighs.
Halfway across the bridge a 30 gram sparrow lands on the cab, but the
bridge doesn't collapse. Why not?
Since the bridge is 4 kilometers
long, the halfway point would be 2 kilometers. The 18-wheeler would
have used much more than 30g of fuel to drive 2 kilometers.
A completely black dog was strolling down Main street during a
total blackout affecting the entire town. Not a single streetlight had
been on for hours. As the dog crosses the center of the road a Buick
Skylark with 2 broken headlights speeds towards it, but manages to
swerve out of the way just in time. How could the driver see
the dog to swerve in time?
Ida puts her coffee into the microwave, as she does every morning,
for exactly 2 minutes. When the microwave goes off, she opens the door,
but then closes the door again and sets the microwave for 2 more seconds.
What good would 2 more seconds be?
You are a cook in a remote area with no clocks or other way of keeping time other than a four-minute and a seven-minute hourglass. On the stove is a pot of boiling water. Jill asks you to cook a nine-minute egg in exactly 9 minutes, and you know she is a perfectionist and can tell if you undercook or overcook the egg by even a few seconds. How can you cook the egg for exactly 9 minutes?
1. Flip both hourglasses over and drop the egg into the water.
2. When the 4-minute timer runs out, flip it over (4 minutes elapsed, 3 remaining on the 7-minute timer).
3. When the 7-minute timer runs out, flip it over. (7 minutes elapsed, 1 remaining in the 4-minute timer)
4. When the 4-minute timer runs out, flip the 7-minute timer over. (8 minutes elapsed. 6 minutes remained in the 7-minute timer, but flipping it over leaves one minute's worth of sand on top. When it runs out exactly nine minutes will have elapsed.
I am the owner of a pet store. If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?
If you put one canary in each cage, you have an extra bird without a
cage. However, if you put two canaries in each cage then you have two
canaries in the first cage, two canaries in the second cage and an
extra cage.
Here is a series of numbers. What is the next number in the sequence? 1 11 21 1211 111221 312211 13112221
The next number in the sequence is 1113213211, because the rule for creating the next number is to simply describe the previous number. The first number is 1, or 1 (one) 1, so you get 11. To describe 11, you have two 1's, or 21. Now you have one 2 and one 1, so the next number is 1211. The solution is to simply continue describing the previous number using only numbers.
My daughter has as many sisters as she has brothers. Each of her brothers has twice as many sisters as brothers. How many sons and daughters do I have?
Four daughters and three sons. Each daughter has 3 sisters and 3 brothers, and each brother has 2 brothers and 4 sisters.
To figure it out mathematically, you could use the following two equations where G = the number of girls and B = the number of boys:
G - 1 = B
2(B - 1) = G
Solving for G gives you 4 and plugging that in to G - 1 = B gives you a B of 3.
What seven-letter word has hundreds of letters in it?
Two women apply for a job. They are identical and have the same
mother, father and birthday. The interviewer asks, "Are you twins?"
to which they honestly reply, "No".
You are standing outside a closed door. On the other side of the
door is a room that has three light bulbs in it. The room is completely
sealed off from the outside. It has no windows and nothing can get in or
out except through the door. On the outside of the room there are three
light switches that control each of the respective light bulbs on the
other side of the door.
Your assignment is to determine which light switch controls which light
bulb. You are allowed to enter the room only once, and once you come
out, you must be able to state with 100% certainty which light switch
controls which light bulb.
Turn one light switch on, wait a few minutes, then turn it off and turn
another light switch on. Go into the room and feel the light bulbs.
The one that's still warm is connected to the switch that you first
turned on, the one that is on was the second switch you turned on, and
the last bulb is controlled by the switch that you didn't touch.
If a bottle and a cork cost a dollar and a nickel, and the bottle
costs a dollar more than the cork, how much does the cork cost?
Most people guess 5¢, but $1 more than 5¢ is $1.05, and if the
bottle cost $1.05, the bottle and the cork would be $1.10, not $1.05.
The cork actually costs 2½¢ and the bottle costs a
dollar more, or $1 and 2½¢, making the total $1.05.
A boat has a ladder that has six rungs. Each rung is one foot apart.
The bottom rung is one foot from the water. The tide rises at 12 inches
every 15 minutes. High tide peaks in one hour.
When the tide is at its highest, how many rungs are under water?
None. The boat is floating on the water, so as the tide rises, so does
the ladder.
You have a lighter and two fuses that take exactly one hour to
burn, but they don't burn at a steady rate. For example, one fuse
could take 59 minutes to burn the first inch and then burn the rest
of the fuse in the last minute.
How would you use these two fuses to measure 45 minutes?
Light the first fuse on both ends and the second fuse at only one end.
When the first fuse burns out you know 30 minutes have passed. Light the
other end of the second fuse and when it burns out, 45 minutes have passed.
You have two buckets - one holds exactly 5 gallons and the other
3 gallons. How can you measure 4 gallons of water into the 5 gallon
bucket?
(Assume you have an unlimited supply of water and that there are no
measurement markings of any kind on the buckets.)
Pour the 3 gallons of water into the 5-gallon bucket
Fill the 3-gallon bucket again.
Fill up the 5-gallon bucket with the 3-gallon bucket, leaving you with 1 gallon left in the 3-gallon bucket.
Empty out the 5-gallon bucket.
Pour the remaining 1 gallon of water from the 3-gallon bucket into the 5-gallon bucket.
Fill the 3-gallon bucket.
Pour the 3 gallons of water from the 3-gallon bucket into the 5-gallon
bucket leaving you with 4 gallons of water in the 5-gallon bucket.
Alternate solution:
Fill up the 5 gallon bucket
Pour it into 3 gallon bucket, leaving 2 gallons
Empty out the 3 gallon bucket
Pour the 2 gallons in the 5 gallon bucket into the 3 gallon bucket
Fill up the 5 gallon bucket and pour it into the 3 gallon bucket until it's full, leaving 4 gallons in the 5 gallon bucket.
A princess is as old as the prince will be when the princess is
twice the age that the prince was when the princess's age was half the
sum of their present ages.
This one took a while, but I figured it out. You can
find the answer here.
During WWII, there was a bridge connecting Germany and Switzerland,
and on the German side, there was a sentry tower with a guard in it.
He would come out every three minutes to check on the bridge, and he had
orders to turn back anyone who tried to get into Germany, and shoot
anyone trying to escape without a pass. There was a woman who
desperately needed to get into Switzerland, and she knew she didn't
have time to get a pass. It would take her at least six minutes to
cross the bridge, but she managed to do it. How?
She walked on the bridge towards Switzerland for 3 minutes and just
as the guard was about to come out, she turned around walking back to
Germany. The guard saw her and asked for her pass but she didn't have one
and was sent back (or what the guard thought was back) to Switzerland.
In her case it was the very country she wanted to go to.
A man can make perfect counterfeit bills. They look exactly like
real ones, they're made of exactly the same materials, made the same way,
everything. So perfect, one could pretty much call them real bills.
One day he successfully makes a perfect copy of another bill. However,
he gets caught when he tries to use the copy. How is this possible?
You will hang me. If they hang him, then the statement was true and they could only hang him for telling a lie. If they shoot him, then it makes the statement a lie and they were only to shoot him for telling the truth. An alternate solution is to say, "You will not shoot me," leading to the same quandary for the killers.
How many people can read hex if only you and dead people can
read hex?
The trick is that the word dead represents a number in
hexadecimal. That number in base 10, plus one to include
yourself, is: 57005 + 1 = 57006.
A man is traveling with a fox and two chickens, if he leaves the
fox alone with the chickens the fox will eat the chickens. He comes to a
river and needs to cross it, he finds a small boat that can carry only
him and one animal, how does he get himself, the fox and two chickens
across the river safely?
Take the fox over, return with nothing. Go over with one chicken,
return with the fox. Go over with the second chicken, return with
nothing. Finally, take the fox over.
A man is looking at a picture of a man on the wall and states:
Brothers and sisters I have none, but this man's father is my father's
son. Who is the man in the picture in relation to the man looking at
the picture?
The man in the picture is his son. Since he doesn't have any brothers
or sisters, the statement my father's son is himself.
A shortened version would be this man's father is myself, so he is the
father of the man in the picture.
A man and his son had a terrible car accident and were rushed
to the hospital. The man died on the way, but the son was still barely alive.
When they arrived, an old gray surgeon was called in to operate. Upon seeing the young boy, the surgeon said, "I can't operate - this is my son."
How is this possible?
A wise king devised a contest to see who would receive the
Princess' hand in marriage. The Princess was put in a 50 x 50 foot
carpeted room. Each of her four suitors were put in one corner of the
room with a small box to stand on. The first one to touch the Princess'
hand would be the winner and become the new King.
The rules were the contestants could not walk over the
carpet, cross the plane of the carpet, or hang from anything; nor could
they use anything but their body and wits (i.e. no magic, telepathy, nor
any items such as ladders, block and tackles etc).
One suitor figured out a way and married the Princess and became the
new King. What did he do?
Two guards were on duty outside a barracks. One faced up the road
to watch for anyone approaching from the North. The other looked down the
road to see if anyone approached from the South. Suddenly one of them
said to the other, "Why are you smiling?"
They were facing each other. As to why his companion was smiling, the
world may never know.
You're riding a horse. To the right of you is a cliff and in
front of you is an elephant moving at the same pace and you can't
overtake it. To the left of you is a hippo running at the same speed
and a lion is chasing you. How do you get to safety?
You have 50 quarters on the table in front of you. You are
blindfolded and cannot discern whether a coin is heads up or tails up by
feeling it. You are told that x coins are heads up, where 0 < x < 50.
You are asked to separate the coins into two piles in such a way that the
number of heads up coins in both piles is the same at the end.
You may flip any coin over as many times as you want. How will you do it?
Take x coins, flip all of them and put them in one pile. The rest of the
coins form the second pile.
You have four chains. Each chain has three links in it. Although
it is difficult to cut the links, you wish to make a single loop
with all 12 links. What is the fewest number of cuts you must make to
accomplish this task?
3 cuts. Cut each link in one chain. Separate them, and use the links
to join the ends of the 3 intact chains.
Walking down the street one day, I met a woman strolling with her
daughter. "What a lovely child," I remarked. "In fact, I have two
children," she replied. What is the probability that both of her
children are girls?
1/2 probability. There was a raging debate on this brain teaser,
which I got from 3quarksdaily, and after many comments, the
conclusion was that the problem is stated poorly, but there is a
1/2 probability that both of her children are girls.
Three closed boxes have either white marbles, black marbles or
both, and they are labeled white, black and both. However, you're
told that each of the labels are wrong. You may reach into one of the
boxes and pull out only one marble. Which box should you remove a
marble from to determine the contents of all three boxes?
The one labeled both. Since you know it's labeled incorrectly, it
must have all black marbles or all white marbles. After you determine
what it contains, you can identify the other two boxes by the process
of elimination.
A glass of water with a single ice cube sits on a table.
When the ice has completely melted, will the level of the water have
increased, decreased or remain unchanged?
The water level remains unchanged because the ice cube displaces its own weight. If you're not convinced, read Archimedes' Principle, which states that any floating object displaces its own weight of fluid. Still not convinced? Here are a few moresources .
You are given eight coins and told that one of them is counterfeit.
The counterfeit one is slightly heavier than the other seven. Otherwise,
the coins look identical. Using a simple balance scale, how can you determine
which coin is counterfeit using the scale only twice?
First weigh three coins against three others. If the weights are equal,
weigh the remaining two against each other. The heavier one is the
counterfeit. If one of the groups of three is heavier, weigh two of
those coins against each other. If one is heavier, it's the
counterfeit. If they're equal weight, the third coin is
the counterfeit.
I was visiting a friend one evening and remembered that he had
three daughters. I asked him how old they were. "The product of their
ages is 72," he answered. Quizzically, I asked, "Is there anything else
you can tell me?" "Yes," he replied, "the sum of their ages is equal
to the number of my house." I stepped outside to see what the house
number was. Upon returning inside, I said to my host, "I'm sorry, but I
still can't figure out their ages." He responded apologetically,
"I'm sorry, I forgot to mention that my oldest daughter likes strawberry
shortcake." With this information, I was able to determine all three
of their ages. How old is each daughter?
3, 3, and 8. The only groups of 3 factors of 72 to have non-unique sums
are 2, 6, 6 and 3, 3, 8 (with a sum of 14). The rest have unique sums:
2 + 2 + 18 = 22
2 + 3 + 12 = 18
2 + 4 + 9 = 15
3 + 4 + 6 = 13
The house number alone would have identified any of these groups. Since more information was required, we know the sum left the answer unknown. The presence of a single oldest child eliminates 2,6,6, leaving 3,3,8.
You're in a room with two doors. There's a guard at each door. One
door is the exit, but behind the other door is something that will kill
you. You're told that one guard always tells the truth and the other guard
always lies. You don't know which guard is which. You are allowed to ask
one question to either of the guards to determine which door is the exit.
What question should you ask?
Ask either guard what door the other guard would say is the exit, then
choose the opposite door.
If you ask the guard who always tells the truth, he knows the other guard
would lie, so he'll point you to the door leading to death. If you ask
the guard who always lies, he knows the other guard would truthfully
show you the exit, so he'll lie and point you to the door leading to
death.
An alternate solution is to ask a guard what they would answer if you were to ask them which door was the exit, then choose that door. The truthful guard will point to the correct exit, but the lying guard will too. Here's why. If you asked him what door was the exit, he would normally lie and point to the death door, but you asked him what he would say if you asked what door was the exit, and in order to lie to that question, he will point you to the exit.
240. To get the number, multiply the previous number in the series by its position. 48 is in the 5th position, so 48 × 5 = 240
You are a prisoner sentenced to death. The Emperor offers you a
chance to live by playing a simple game. He gives you 50 black marbles,
50 white marbles and 2 empty bowls and instructs you to divide the 100
marbles into the two bowls. You can divide them however you want as long
as all the marbles are in the bowls. You will be blindfolded and the bowls and marbles will be throughly mixed. You will then choose a single marble from one of the bowls. If the marble is white, you live. Black and you will be put to death.
How do you divide the marbles up so that you have the greatest
probability of choosing a white marble?
Place 1 white marble in one bowl, and place the rest of the marbles in
the other bowl (49 whites, and 50 blacks).
This way you begin with a 50/50 chance of choosing the bowl with one
white marble and living. Even if you choose the other bowl, you still
have an almost 50% chance of picking one of the 49 white marbles. There
are no guarantees in life, but this is your best bet at surviving.
What is the next number in this series? 1, 2, 6, 42, 1806?
To get the next number, multiply the previous number in the series by itself plus one: n * (n+1). For example, to get 6, multiply 2 * 2+1. To get 42 multiply 6 * 6+1. Thus, 1806 * 1807 = 3263442
You must buy 100 chickens for exactly $100, and purchase at least one chicken from each store. The first store charges 5 cents/chicken, the second charges $1/chicken and the third charges $5/chicken. How many chickens should you buy from each store?
The missing numbers are 4 and 9. The list is sorted alphabetically by
the English spelling of the numbers, so four belongs after five and nine
comes after fourteen.
What 4-digit number abcd satisfies this equation?
4 * abcd = dcba
Bill buys three items at the store for exactly $100. The second
item costs half as much as the first item, and the third item is half
as much as the second. How much did each one cost?
A man was killed on Sunday morning. His wife found the body and called the police. The police arrived and questioned the chef, maid, butler, and gardener. Their alibis were:
Chef - making breakfast
Maid - getting mail
Butler - setting table
Gardener - watering plants
The police immediately arrested the criminal. Who was it and how did they know?
This is an unusual paragraph. I'm curious as to
just how quickly you can find out what is so unusual
about it. It looks so ordinary and plain that you
would think nothing was wrong with it. In fact,
nothing is wrong with it! It is highly unusual though.
Study it and think about it, but you still may not
find anything odd. But if you work at it a bit, you
might find out. Try to do so without any coaching.
The letter e is the most common letter in the English language, yet it never appears in the entire paragraph
A murderer is condemned to death. He has to choose
between three rooms. The first is full of raging fires,
the second is full of assassins with loaded guns, and
the third is full of lions that haven't eaten in 3
years. Which room is safest for him?
There are six glasses in a row. The first three are full of water, and the next three are empty. By moving only one glass how can you make them alternate between full and empty?
Three numbers, 16, 14 and 38, need to be assigned to one of the rows of numbers below. Where do the numbers belong? (Hint: This is not a mathematical problem. The numerical values are irrelevant)
Pressing these digits in sequence will produce HELLO WORLD on a cell phone (for an SMS text message)
Two men are standing on one side of a bridge and two women are approaching them. One of the men says, "Here comes my wife and daughter" to which the second man replies, "Here comes my wife and daughter". If they have not married the same woman and the women aren't pregnant, how is this true?
A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?
Rhonda will go see ballet but not the opera. Her favorite number is eight and she doesn't like nine. She likes salmon but not trout. She hates Mondays and likes Wednesdays. Does she use a comb or a brush?
A man leaves home, turns left, goes straight, turns left again, goes straight and turns left once more then returns home and there's another man with a mask on. What's going on?
A man is leaving on a business trip and stops by his office on the way to the airport. The night watchman stops him and says, "Sir, don't take that flight. I had a dream last night that your plane would crash and everyone would die!" The business man cancels his trip and sure enough, the plane crashes, killing all the passengers. The man gives his watchman a $10,000 reward for saving his life, then fires him. Why?
One thousand (or one hundred and one, depending on how you pronounce it)
A sharpshooter hangs up his hat, turns around and walks 50 meters, then turns around and shoots his gun, putting a hole right through his hat. How did he do it?
Look in the mirror, then at the wall and back at the mirror to see what you saw. Use the saw to cut the table in half and join the two halves to make a whole. Put the "hole" on the wall and climb out. (I know, it's lame. I like to have brain teasers that you can realistically guess, but this one's so popular, I feel an obligation to include it.)
There's a green ranch house on a green street with green walls, tables and chairs. What color is the staircase?
A man saw a snake crossing the road and swerved to crush it with his tires. All the street lights were off as well as the car's headlights. There were no other lights on along the road. How did the man see the snake?
Four cards are placed in front of you on the table, each with a number on one side and a color on the other. The visible cards show 3, 8, red and brown. Which cards should you turn over in order to test the truth of the statement that if a card shows an even number on one face, then its opposite face is red?
You'd need to turn over only the 8 and brown card. Only a card with an even number on one face and which is not red on the other face can invalidate the stated rule. If you turn over the 3 card and it's not red, it doesn't invalidate the rule, nor does turning over the red card and finding it has the label 3.
This test was devised by Peter Cathcart Wason and is known as the Wason selection task. Less than 10% of test subjects got it correct in two separate studies.
What do the following words have in common?
current, by, dew, faze, loan, ate
5 4 5 + 5 = 550
Add a diagonal line on the top left of the first plus sign to convert + into a 4. You could also put a slash through the equal sign to make ≠ (not equal) but that's not as cool.
During lunch hour a group of boys from Mr. Bryant's homeroom visited a nearby grocery store. One of the five took an apple.
Jim said, "It was Hank or Tom".
Hank said, "Neither Eddie nor I did it."
Tom said, "Both of you are lying."
Don said, "No, one of them is lying, the other is speaking the truth."
Eddie said, "No, Don, that is not true."
When Mr. Bryant was consulted, he said, "Three of these boys are always truthful but two will lie every time."
Who took the apple?
Tom took the apple
Jim was telling the truth
Hank was telling the truth
Tom was lying
Don was lying
Eddie was telling the truth
(3 telling the truth and 2 lying)
A six-digit number represented by ABCDEF (each letter represents a different number) can be multiplied by 2, 3, 4, 5, and 6 and yet no new digits appear in the result. As a matter of fact, all the digits are rotated. What is the number?
Fish. The gh is pronounced as in tough, the o as in women and the ti as in nation. Ghoti is a constructed word to illustrate irregularities in English spelling.
675. The next number in the sequence is n squared minus m or f(n,m) = n2 - m
f(6,9) = 62 - 9 = 27
f(9,27) = 92 - 27 = 54
f(27,54) = 272 - 54 = 675
f(54,675) = 542 - 675 = 2241
Two boys weighing 50 pounds each and their older brother weighing 100 pounds wish to cross a river. Their boat will only hold 100 pounds. How can they all cross the river in the boat?
Two 50lb boys cross, one comes back.
100lb boy crosses, other 50lb boy returns
Both 50lb boys cross.
A circular island with a diameter of 30 feet has a 30 foot tree stands at the center. A man cuts the tree down with his chainsaw, making the cut a foot up from the ground. The tree comes crashing down and hits the water but doesn't splash. Why not?
Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?
A) Yes
B) No
C) Cannot be determined
91. To get the number in the fourth column, you add the numbers in column 1 and 2, then multiply by the number in column 2. f(n,m) = (n + m) * m
For example, f(2,3) = (2 + 3) * 3 = 15. Thus f(6,7) = (6 + 7) * 7 = 91
Two scruffy dogs were walking down the street. The first dog turned to the other and said, "Do you realize that if one of your fleas jumped onto me we would have the same number of fleas?" The second replied, "Yes, but if one of your fleas jumped onto me I would have five times as many fleas as you." How many fleas are on each dog to begin with?
A snail creeps 10 feet up a wall during the daytime, then falls asleep. It wakes up the next morning and discovers it slipped down 6 feet. If this happens each day, how many days will it take to reach the top of a 22 foot wall?
4 days
Day 1: up to 10, down to 4
Day 2: up to 14, down to 8
Day 3: up to 18, down to 12
Day 4: up to 22 (20 really) and done
Two children were playing checkers and each played five games. Both children won the same number of games yet there were no ties. How is this possible?
Put 7 pigs in the first three pens and arrange the fourth pen to contain the other three pens.
A woman gave a man a list of things she needed to buy at the store. The man gave the list back to the woman and she turned red with embarrassment. Why?
The man was a checkout clerk at the grocery store. The list was for items to get at a lingerie store.
Mike, Jimmy, Nader, Kevin, and Larry were the top five finishers in the regional 500-mile race. They drove yellow, orange, green, red and blue cars but not necessarily in that order. Neither Kevin nor Larry drove the green car. Kevin finished faster than Mike and Larry. The blue car finished earlier than Larry's and Nader's car. The yellow car finished faster than the green car and the orange car. Mike's and Larry's car finished ahead of the orange car. Jimmy's car finished before the blue and the yellow car. Who drove what color car and what place did each driver finish?
1st - Jimmy, red car
2nd - Kevin, blue car
3rd - Larry, yellow car
4th - Mike, green car
5th - Nader, orange car
While driving his car a man slams on the brakes when he sees, in the middle of the street, a diamond studded door, a gold door and a silver door. Which door does he open first?
Ronald has a rare opportunity to meet the President of the United States. During his visit the president gives him a gift but tells Ronald he is never to sell it unless he sees the president again. Ronald consents, but the president dies later that year. Years later a man offers to buy the President's gift for $1000. Ronald agrees and exchanges the gift for 20 crisp $50 bills. Did he keep his promise?
Yes. The president was Ulysses S. Grant, who died in 1885 and whose face has been on the $50 bill since 1913. He saw the president on the bills before he made the exchange.
What 3 digit number has a tens digit that is 5 more than the ones digit and a hundreds digit that is 8 less than the tens digit?
Eat (8) flush (plus) to (2) my nose (minus) tree (3) times (times) for (4) they buy dead by (divided by) too (2).
There are two answers depending on whether you calculate as you read or calculate the entire solution at the end.
8 + 2 = 10, - 3 = 7, x 4 = 28, / 2 = 14
or
8 + 2 - 3 x 4 / 2 = 10 - 6 = 4
A man owed his friend $63 and repaid him the exact amount in cash without using coins or $1 bills (no online transfers, checks, credit cards or any other tricks) and without requiring change. How did he do it?
A vile old woman on evil bent, picked up her veil and away she went. “Levi my son” she was heard to say, “what shall we do to live today?”
Perform this calculation in your head, mentally adding the numbers as quickly as you can. Start with 1000 and add 40. Now add 1000. Add 30 to that, then add another 1000. Now add 20 to that result. Add another 1000 and finally, add 10 to that. What is the total?
The taxi driver is not in his cab, he's out for a run. The house he went through was his own because he was done running.
Suppose you have twelve eggs and a balance scale. All of the eggs are identical except for one whose only difference is its weight. Using the scale only three times, determine which egg is the odd egg out and whether it is heavier or lighter than the other eggs.
Weigh four against four. If they're equal, weigh three of them against three you haven't weighed. If they balance too, weigh the last remaining egg against any of the others to see if it is lighter or heavier. If the three suspects are heavier, weigh one of them against another and the one that goes down is it. If they balance the remaining suspect is heavy. Use the same process if they're lighter. If the initial four vs four don't balance, weigh two heavy eggs and a light egg against one heavy egg, one light one and a known normal egg. If they balance weigh the remaining two light eggs against each other. If they balance the unweighed heavy egg is the odd one out. If the side with two heavy eggs goes down weigh them against each other. If they balance it is the light egg on the other side. If the other side goes down it is either because of one heavy egg on that side or because the one light egg on the other side is lighter than the rest. Weigh one of them against a known normal egg to determine which is true.
What number belongs at the beginning of this sequence?
?, 3, 2, 3, 9, 2, 4, 8, 4, 3, 7, 6
If you break up the numbers into groups of 4, a,b,c,d, then 2 × |a - d| = |b - c|.
9 2 4 8 → 2 × |9 - 8| = |2 - 4|, or 2 × 1 = 2
4 3 7 6 → 2 × |4 - 6| = |3 - 7|, or 2 × 2 = 4, so
n 3 2 3 → 2 × |3 ½ - 3| = |3 - 2|, or 2 × ½ = 1;
I'm not sure this is the correct solution, but it's the best I've found so far. Email me if you know of a better one.
Imagine you're alone in a boat with a large hole in the bottom. Sharks are swimming around you on all sides and the boat is sinking fast. How do you survive?
3:36pm. For every 60 minutes of real time, the clock moves 50 minutes. Put another way, 60/50 = 1.2 real minutes per slow-clock minute. In order for the clock to show 3:00pm, 180 of its slow minutes have to pass. 1.2 * 180 clock minutes = 216 real minutes or 3 hours and 36 minutes.
A man is running across a field at night clutching something in his arms as several other men pursue him. He looks back and sees they're getting closer. In a final burst of effort his pursuers catch up and bring him crashing to the ground. His pursuers stand over him but do not touch him or take what he was carrying. Why not? Who was the running man?
Two cowboys live next door to each other and both have a corral for their cows in the back. One day they meet at the back of their homes, standing next to a wall dividing their corrals. The first cowboy gets to thinking and asks his neighbor for a cow so he can double his herd. The other cowboys replies, "That's fine by me partner, cuz then we'll have the same number of cows?" How many cows does each cowboy own?
We'll use A to represent the first cowboy and B for the second cowboy.
A + 1 = 2A, so A = 1. A + 1 = B - 1, so B = 3.
On a dark, stormy Halloween night, four kids named Luke, John, Sarah and Bob walk into a haunted house during a blackout. Only one can escape. They take a staircase to the second floor, a trapdoor on the left, then go up the ladder to the right, followed by a 28-foot slide to the basement through the mouth of a Giant Panda. In one corner of the murky cellar is a chainsaw, a dagger, a rope with a noose and an electric chair. Written on the wall in blood are the words, "Only one will survive - choose your death!" Bob takes the rope, Sarah picks up the dagger, John chooses the chainsaw and Luke uses the chair. Who survives?
A red-house is made of red bricks, has a red wooden door and a red roof. A yellow-house is made of yellow bricks, has a yellow wooden door and a yellow roof. What is a green-house made of?
On a game show there are three closed doors - one hides a car and the other two conceal a goat. The contestant selects a door, which remains closed, and the host, knowing where the car is hidden, reveals a goat behind one of the remaining two doors. The contestant is then given the option to switch doors or stay with the one they originally selected. What should the contestant do to have the best chance of winning the car?
The contestant should switch doors, which doubles the chance of winning the car. Initially there is a 2/3 chance of picking a goat, but once the other goat is revealed, switching to remaining door gives the contestant a better chance of winning the car. This is known as the Monty Hall Problem and can be very unintuitive.
If a plane sits on a conveyer belt whose speed matches that of the plane in the opposite direction, can the plane take off?
Yes, because a plane's wheels roll freely and have no affect on the movement of the plane(unlike a car). The propellor or jet engine makes the plane move and the plane will be able to take off normally. If you don't believe me, here's proof.
Go back. You must strive to find a way to stay alive. What is 4+no.5?
Three rooms contain, 1) Gold coins, 2) Currency notes and 3) Cotton bags. If all three rooms catch fire, which room will the ambulance pour water on first?
Alfred and Bill are clerks at the local grocery store. Alfred can stock a shelf in 20 minutes, but Bill is new and takes 30 minutes. How long would it take for them to stock a shelf together?
Working together they can stock a shelf at a rate of 1/20 + 1/30 (or 5/60) per minute. They'll finish in 12 minutes
Ralph goes to the hardware store to buy something for his house. He asks the clerk how much one will cost and the clerk looks it up and tells him it will be $3. He asks about buying twelve and is told it will be $6. Two hundred will cost $9. What is Ralph buying?
(7 x 7 x 7) + (9 x 9 x 8) + ((9 - 8) x 8) = 999
If other operators were allowed, another solution would be 999 modulo (888 x 777)
This problem can be solved by pre-school children in five to ten minutes, by programmers in an hour and by people with higher education...well, check it yourself.
Jim and Wanda both have some apples. If Jim gives Wanda an apple, they will both have the same number of apples. However, if Wanda gives Jim an apple, Jim will have twice as many as Wanda. How many apples do Jim and Wanda each have?
A fine chap with a blind nephew (or an exemplary uncle who died before his nephew was born).
From a basket of mangoes when counted in twos there was one extra,
counted in threes there were two extra,
counted in fours there were three extra,
counted in fives there were four extra,
counted in sixes there were five extra,
but counted in sevens there were no extras.
At least how many mangoes were there in the basket?
119.
The number has to be evenly divisible by seven for there to be no extras when counting in sevens, and it has to be odd in order for there to be one extra when counting by twos. It also can't be evenly divisible by three through six. 119 is the first odd multiple of 7 that satisfies the requirements.
Aside from the potential response that it's rude to ask the age of a lady, the answer can be worked out mathematically.
x + 2 = 2(x - 5)
x + 2 = 2x - 10
x + 12 = 2x
12 = x
In two years she'll be 14, which is twice her age 5 years ago (7).
The 17 items in your shopping cart weigh 8 pounds. But when your daughter puts in a ball, poster board and yo-yo the shopping cart weighs less. How is that possible?
She gave the same 2 apples to each child in succession.
A dad offered to pay his son $5 for every correct answer on his math test. His son said he would pay his Dad $8 for every incorrect answer. There were 26 questions on the test and no money was exchanged. How?
The son got 16 questions correct and missed 10. This means he owed his Dad 10 * $8 = $80, but his Dad owed him 16 * $5 = $80, so it was a wash.
Two math equations to solve it are x + y = 26 and 5x = 8y.
If two hours ago it was as long after one o'clock in the afternoon as it was before one o'clock in the morning, what time is it right now?
9pm (or 21:00). There are 12 hours between 1pm and 1am, so 6 hours after 1am is halfway. 6 hours + 1pm equals 7pm. In order for 7pm to be 2 hours behind the current time, it must be 9pm.
A man walks out of a house that has four walls all facing north. A bird walks past him. What kind is it?
A penguin. If all four walls face north the house must be at the southernmost point of the earth. Really, any native antarctic bird would work.
This brain teaser is quite similar to the guy whose house walls face south and sees a bear, then you're asked the color of the bear. The bear would be white (a polar bear) as they're the only bears indigenous to the north pole. A lawyer would claim it's all circumstantial evidence and the bear could be an imported brown bear. The laywer makes a valid point.
What is the longest word in the English dictionary?
It's a palindrome (a word or phrase that's spelled the same backwards and forwards).
A man gets off the bus looking for an address and approaches a couple walking in the same direction for directions. The woman says they're going that way and take him. Along the way the man asks if they're related. The woman grins and says, "We're not strangers. This man's mother is my mother's mother-in-law." The man is confused but doesn't say anything. When he gets back home he tells his wife about the conversation and she can't figure it out either. They decide to ask their lawyer and he eventually works it out with pen and paper. How are the couple related?
The couple is either a man and his daughter or an uncle and his niece.
A dad told his son he would give him $5 for every correct answer on his math test. His son replied that he would pay $8 for every incorrect answer. There were 26 questions on the test and no money was exchanged. Why?
Phil asks his friend Stan when his birthday is. Stan replies that he was 32 the day before yesterday and next year he'll be 35. When is his birthday and how is this possible?
Today is Jan 1st and his birthday is on December 31st. He was 32, then turned 33 on Dec 31st, and this year on Dec 31st he'll turn 34, so next year he'll be 35.
A man wants to get into a night club where the bouncers test each person before they can enter. The man waits and watches. A woman walks up to the bouncers and the bouncers say 6. The woman replies with 3 and goes in. A small man walks up and they say 12. The man replies 6 and is admitted. The first guy thinks he's figured it out and walks up. They say 4 and the man replies with 2, but they don't let him in. What should he have said?
A similar problem can be found in L.A. Graham's Ingenious Mathematical Problems and Methods with a range of 1 to 9, but the principle remains the same - the numbers with the smallest difference produce the largest product. You start out with the highest two digits, 7 and 6, then attach 5 and 4, putting the smaller of the two digits with the larger number, giving you 74 and 65. The next two highest digits are 3 and 2, giving you 742 and 653. Finally, you add the 1 to the lower number. Page 80 has the details of that solution.
I have nine matchbox sticks and would like to make ten. How do I do it?
Arrange the nine matchbox sticks like so to make the shape of the number ten:
_
/| | |
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In 2012 a class was divided into 2 groups. Their assignment was to find the names of at least 3 children who were born on the same day from 5 different months of 2011. These were the results:
Group 1
August 20: Oliver, William, and Adam.
January 3: John, Alice, and Ken.
September 7: Bruce, Shane, and Peter.
June 11: April, Patrick, and Bobby.
July 19: Trent, Julie, and Charles.
Group 2
March 1: Karl, Willie, and Patty.
February 29: Blake, Kobe, and Wayne.
December 24: Kyle, Chad, and Zoe.
May 12: Matthew, Manny, and Adrian.
November 20: Greg, Fiona, and Elizabeth.
The members of group 2 got an F on the assignment. Why?
She will always need to give you 5 apples. You both need at least 5 apples to begin with, but apart from that it doesn't matter exactly how many you each have. When she gives you 5 you will have 10 more than her because she will lose 5 and you will gain 5, resulting in a net difference of 10.
For example, if you each have 25 apples and she gives you 5 of hers, she will be left with 20 and you will now have 30, precisely 10 more than she has.
The most popular answer for this teaser is 'today'. Of course this only works if you're reading it on that particular date or if the date is not specified. Another option is to respond literally with 'a date'. Lastly, certain dates could be squeezed into letters using Roman numerals if you abbreviate the year to 2 numerals. For example, January 20th, 2011 would be I XX XI.
How can the numbers 6, 1, 7 and 9 be arranged to make 24?
1020. There are 6 men with 2 legs each, for a total of 12 legs.
There are 36 cats with 4 legs each for a total of 144 legs.
There are 216 kittens with 4 legs each for a total of 864 legs
12 + 144 + 864 = 1020.
Three ants are walking in the same direction. The first ant has two ants behind him, the second ant has one in front and one behind, but the third ant has one in front and one behind too. How is this possible?
The ants are in a circle. Lets say the ants are A, B and C. A has has B and C behind him, B has A in front and C behind, and C has B in front and A behind.
You are a spy and need to send an item to a contact in another country without letting anyone else have access to it. All unlocked items will be opened in transit. How can you send this item securely?
Place a lock on the item and send it to your contact. They will place their own lock on the package and return it to you. You remove your lock and send it back. When they receive it, they can unlock the package and retrieve the item.
The aunt of all of her cousins is Dina's own mother.
A zebra was going to the river. On the way the zebra encountered five giraffes. Each giraffe had five monkeys on their neck. How many animals were going to the river?
The word rendezvous. Even though it's a French word, it's in the English dictionary and is pronouced [rahn-duh-voo].
James makes a bet with Laura that he can use any name she can think of in a song she will recognize with the original lyrics. Laura takes him up on the bet and loses. What song did James sing to win?
"Won spawn amid niger eerie" sounds like, "Once upon a midnight dreary", from The Raven by Edgar Allan Poe.
At the market you can buy a cow for $10, a pig for $1 and 8 hens for $1. How many animals would you need to buy to get 100 mixed animals for exactly $100?
7 cows, 21 pigs and 72 hens. The trick to this is finding the combination of cows and hens with the same cost and quantity since pigs are already equal. The magic combination is 7 cows and 72 hens, giving you 79 animals that cost $79 ($70 + $9). Then you just add 21 pigs to get to 100 animals.
A man goes to bed at 9:45 pm. He makes himself a drink, then turns off the TV and the lights. The night was windy and there was a major storm. The next day he discovers he was the cause of seven deaths. How is this possible?
He lived in a lighthouse as lighthouse keeper. He turned off all the lights by accident, so a ship with 7 passengers couldn't negotate the rocky shores. One would think the light switches in a lighthouse would be more clearly marked.
An electric train is traveling on a 2000-mile journey from Chicago, IL to Los Angeles, CA. It has 16 cars with a total of 320 passengers. The weather is cloudy and cool, with a warm front approaching from the south. Which direction will the steam blow?
Franklin lent Darlene as much money as she already had, then she spent $10. The next day, Franklin lent her as much money as she now had and again, she spent $10. On the third day Franklin once again lent her as much money as she now had and she spent $10, leaving her broke. How much money did Darlene start with?
$8.75 You may have been tempted to guess $30 because $10 is spent three times, but that would mean she would have had $60 ($30 lent plus the $30 she already had), and $50 after spending $10. The rest of the numbers end up at higher than zero, so we know it has to be less than $30. Even starting at $10 leaves Darlene with $10 on the third day. Starting with $8.75 works out as follows.
9. If all but 9 died, there are 9 remaining live sheep.
There was a neighborhood of one-story houses.
One was red and everything in the house was red.
Another was purple and everything in the house was purple.
Yet another was yellow and everything in the house was yellow.
Still another was blue and everything in the house was blue.
In the green house everything was greeen,
and in the gray house everthing was grey.
What color were the stairs in the yellow house?
In-laws. The word in is found inside the word laws.
Peppino bought a new hat and Tito asked what day he bought it. Peppino replied, "If yesterday was tomorrow, today would be Tuesday." On what day did Peppino buy his hat?
Coffee break. The word coffee is broken into two pieces.
A man hiked through the woods with his dog and saw three coyotes, six wolf cubs, seven bunnies, nine squirrels and thirteen chipmunks. How many total feet were there?
Monkey, donkey, turkey, jockey, hockey, doohickey, malarkey and passkey. There may be others, but you get the drift.
Kevin, Charles, Larry and Alex are in a room that's about 110 feet long. In front of them are 5 balls which are exactly 100ft from the exit. The balls are yellow, purple, green, red and blue, respectively. Each man must carry a ball to the exit. After traveling 20ft a ball will change color twice. The sequence of color changes is always the same: yellow, purple, green, red, and blue.
At 80ft Kevin's ball is red. At 40ft Larry's ball is purple. At 60ft Charles' ball is blue and at 100ft Alex's ball is purple.
What color ball was left behind?
The remaining ball was blue. Here's a table of each ball and the color it changes to at 20, 40, 60, 80 and 100ft. Kevin's started out yellow, Larry's was green, Charles' was red and Alex began with a purple ball, leaving blue as the one nobody picked.
20ft
40ft
60ft
80ft
100ft
Yellow
Green
Blue
Purple
Red
Yellow
Purple
Red
Yellow
Green
Blue
Purple
Green
Blue
Purple
Red
Yellow
Green
Red
Yellow
Green
Blue
Purple
Red
Blue
Purple
Red
Yellow
Green
Blue
Five kinds of flowers grow in separate gardens on five different streets. Here is what you know:
1. The Smiths do not grow violets.
2. The Morgans grow peonies and do not live on 2nd street.
3. The Parks live on 3rd street.
4. Begonias bloom on 4th street.
5. Roses do not grow on 5th street.
6. The Johnsons do not live on 1st street.
7. The Rosens do not grow daffodils
8. The Johnsons grow roses
9. Daffodils grow on 1st street
Which flowers grow on in whose gardens on what streets?
