By moving one of the following digits, make the equation correct. 62 - 63 = 1
26 - 63 = 1
(26 = 2x2x2x2x2x2 = 64, ∴ 64 - 63 = 1)
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?
The eye color of the reader of this problem. The first sentence is the
key: "You are the bus driver"
A rooster lays an egg at the very top of a slanted roof.
Which side is the egg going to roll off on?
Neither, roosters don't lay eggs.
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?
__ __
B| | | |F
A|1 |...........................|10|R
C| | | |O
K| | | |N
|__| |__|T
----------------------------------
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?
The wiseman tells them to switch camels.
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?
It was during the day
In a small cabin in the woods, two men lay dead. The cabin itself
is not burned, but the forest all around is burned to cinders. How did the
men die?
It's the cabin of a plane and the plane crashed.
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?
To rotate the handle on the mug so
she can comfortably remove it.
Beulah died in the Appalachians while Craig died at sea. Everyone
was much happier with Craig's death. Why?
Beulah and Craig were hurricanes.
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?
Four canaries and three cages.
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?
Mailbox
If you had a ton of feathers and a ton of stones which would be
heavier?
Neither. They both weigh a ton.
Tom's mother has three children. One is named April, one is named May. What is the third one named?
Tom
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".
How is this possible?
They are triplets.
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.)
- Fill the 3-gallon bucket.
- 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.
What are their 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?
He made a perfect copy of a counterfeit bill
A prisoner is told "If you tell a lie we will hang you; if you
tell the truth we will shoot you." What can he say to save himself?
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?
The surgeon was his mother.
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?
Asked the princess to touch his hand.
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?"
How did he know his companion was 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?
Get off the merry-go-round.
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 pil
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
more sources .
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.
How far can a dog run into the forest?
Halfway. After that it will be running out of the forest.
What number comes next?
2, 2, 4, 12, 48, ___
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