Brain Teasers
Teaser 1
We'll start it off easy for you! No Peeking!A man has to get a fox, a chicken, and a sack of corn across a river.
He has a rowboat, and it can only carry him and one other thing.
If the fox and the chicken are left together, the fox will eat the
chicken. If the chicken and the corn is left together, the chicken
will eat the corn. How does the man do it?scroll down for answer!
The Answer!
man carries chicken, man leaves chicken and comes back, man gets fox,
man leaves fox and gets chicken, man leaves chicken and gets corn, man
leaves fox and corn to get chicken, man gets chicken.
Teaser 2
A rich old Arab has three sons. When he died, he willed his 17 camels to the sons, to be divided as follows: First Son to get 1/2 of the camels Second Son to get 1/3rd of the camels Third Son to get 1/9th of the camels. The sons are sitting there trying to figure out how this can possibly be done, when a very old wise man goes riding by. They stop him and ask him to help them solve their problem. Without hesitation he divides the camels properly and continues riding on his way. How did he do it?scroll down for answer! The Answer! The old man temporarily added his camel to the 17, making a total of 18 camels.
1/2 = 9
1/3 = 6
1/9 = 2
for a total of 17. He then takes his camel back and rides away......
Teaser 3
An old parchment describes the location of buried treasure thus:
"On the island there are only two trees, A and B, and the remains of a
gallows. Start at the gallows and count the steps required to walk in a
straight line to tree A. At the tree turn 90 degrees to the left and
then walk forward the same number of steps. At the point where you top
drive a spike into the ground. Now return to the gallows and walk in
a straight line, counting your steps, to tree B. When you reach the
tree, turn 90 degrees to the right and take the same number of steps
forward, placing another spike at the point where you stop. Dig at
the point exactly halfway between the spikes and you will find the
treasure."
However, our hero when he gets to the island finds the gallows
missing. Is there any way he can still get to the treasure?scroll down for answer! The Answer!
A simple experiment with a ruler and paper shows that any position for
the gallows leads to the same point. However, it can be proven with a bit of vector algebra...
(best viewed with fixed width font)
Define a square grid with its origin at tree A (herein point A) tree B at
(0,1). Gallows G exist at arbitrary point (x,y).
The walk from G -> A == (-x,-y)
The walk from G -> B == (-x,-y+1)
Let A* denote the position after turning left at tree A, and B* denote
the position reached after turning right at tree B.
The walk from A -> A* == (+y,-x)
The walk from B -> B* == (-y+1,x)
(not entirely obvious, but true!)
The walk from G -> A* == (G -> A) + (A -> A*)
== (-x+y , -x-y )
The walk from G -> B* == (G -> B) + (B -> B*)
== (-x-y+1 , x-y+1)
The walk from A* -> B* == (G -> B*) - (G -> A*)
== (-x-y+1+x-y , x-y+1+x+y )
== (1-2y , 1+2x)
Now, the walk to the treasure is (A->A*) + .5(A*->B*) since the treasure
is half way from A* to B*
== (+y,-x) + .5(1-2y , 1+2x)
== (+y+.5-y , -x+.5+x)
== (.5,.5)
So stand at A, walk half way to B, turn RIGHT and walk the same distance
straight ahead. Get digging.....
Teaser 4
Two men were being tried for murder. The jury found one man guilty and the other innocent. The judge turned to the guilty man and said, "Even though your guilt has been established, the law compels me to set you free." How could such a bizarre judgement occur?scroll down for answer! The Answer!
They were siamese twins!
Teaser 5
In your cellar there are three light switches in the OFF position.
Each switch controls 1 of 3 light bulbs on floor above. You may move
any of the switches but you may only go upstairs to inspect the bulbs
one time. How can you determine the switch for each bulb with one
inspection??scroll down for answer! The Answer!
turn switch 1 on for a while .. about 5 mins or more .. then turn it off.
turn switch 2 on
go inspect
the hot bulb is controlled by switch 1
the lit bulb is controlled by switch 2
the unlit and cold bulb is controlled by switch 3
Teaser 6
How much dirt is in a hole that is 3 ft deep, and 6 inches
in diameter?scroll down for answer! The Answer!
None. A hole only has air in it, no dirt. Sorry that was an easy one!
Teaser 7 1 train leaves from NYC heading towrards LA at 100 mph. three hours later, a train leaves from LA heading towrds NYC at 200 MPH. Assume there's exactly 2000 miles between LA and NYC. When they meet, which train is closer to NYC? scroll down for answer! The Answer! When they meet, they're both at the same spot, so they are both the same distance from NYC.. Teaser 8 Two boxers are in a boxing match (regular boxing, not kick boxing). The fight is scheduled for 12 rounds but ends after 6 rounds, after one boxer knocks out the other boxer. Yet no man throws a punch. How is this possible? scroll down for answer! The Answer! They are female boxers. Teaser 9 In 1990, a person is 15 years old. In 1995 that same person is 10 years old. How is this possible? Yesterdays Solution scroll down for answer! The Answer! The dates are in BC . Teaser 10 There are 3 black hats and 2 white hats in a box. Three men (we will call them A, B, & C) each reach into the box and place one of the hats on his own head. They cannot see what color hat they have chosen. The men are situated in a way that A can see the hats on B & C's heads, B can only see the hat on C's head and C cannot see any hats. When A is asked if he knows the color of the hat he is wearing, he says no. When B is asked if he knows the color of the hat he is wearing he says no. When C is asked if he knows the color of the hat he is wearing he says yes and he is correct. What color hat and how can this be? There is no play on words and there are no tricks. If I used had instead of has it is purely accidental. scroll down for answer! The Answer! A must not see two white hats on B & C, or he would know his own must be black. So his answer establishes that at least one of the hats on B & C is black. If B saw that C was wearing a white hat, then B would know his own was black. Since B could not say that truthfully, then C must be wearing black and he answers so correctly. Teaser 11 A census taker approaches a house and asks the woman who answers the door,"How many children do you have, and what are their ages?" Woman: "I have three children, the product of their ages are 36, the sum of their ages are equal to the address of the house next door." The census taker walks next door, comes back and says, "I need more information." The woman replies, "I have to go, my oldest child is sleeping upstairs." Census taker: "Thank you, I have everything I need." Question: What are the ages of each of the three children? scroll down for answer! The Answer! The Reason the census taker could not figure out the childrens ages is because, even with knowing the number on the house next door there were still two possibilities. The only way that the product could be 36 and still leave two possibilities is if the sum equals 13. These possibilities being 9+2+2 and 6+6+1. When the home owner stated that her "Oldest" child is sleeping she was giving ths census taker the fact that there is an "oldest." The childrens ages are 9,2, &2. Teaser 12 A man has recently escaped from prison and is making his way home on foot. He is walking along a straight rural country lane in bright daylight. He has walked about two miles from the prison, when he sees a police car coming toward him. Despite knowing that all squads would be out looking for him, he ran towards the car for a short while, and only when he was about ten feet away, did he turn and run into the woods to hide. Why did he run towards the police car? scroll down for answer! The Answer! The man is on a bridge when he spots the police car. He's more than halfway across, so the quickest way off the bridge is to run forward. Teaser 13 A heavy truck reaches the edge of a desert which is 400 km wide. It must cross this region, but the vehicle averages only 1 km per litre of fuel, and the total fuel capacity (including extra containers) is only 180 litres, so fuel dumps must be established in the desert in order to make it across. There's plenty of fuel available at the edge of the desert, and you can set up as many fuel dumps as you like. But with proper forethought, what is the least amount of fuel required for the truck to reach the other side? (Forewarned is half an octopus - this is not quite as easy as it might seem to be... unless you approach it from the right direction.) scroll down for answer! The Answer! The "easy" (ha!) way to solve this problem is to work it backwards. A diagram would help, but that would make my explanation more difficult, so activate your imaginations. Consider the greatest distance our truck can travel before all fuel is used: it's 180 km. (1 unit fuel (litre) = 1 unit distance (km)) The optimum solution will have the truck using its last dribble of fuel as it arrives at its destination. Therefore, the last leg will be 180 km. This means that the last (Z) fuel dump must contain sufficient fuel from previous trips plus what's onboard at the last trip to equal 180. In order to get 180 units of fuel to Z, at least 2 other trips are required from some prior dump location. It is safe to assume that the truck made one round trip starting with a full load and returned empty, and that it also made a final one-way trip starting with another full load of 180. (And we don't need to be warp-space scientists to figure out that at least one (hmmm..., why's that, Lem?) additional trip was necessary. In order to cache 180 total units of fuel at this site, the truck used an additional 180 units for travel in three trips, each of which was 60 km. (180/3) This requires that the quantity of fuel at the previous Dump Location = 360. (I'd like to think that there are many mental light bulbs popping on out there... "Oh. Sure. That means...") Moving right along (in a reverse direction, of course,) the previous dump must have had enough fuel cached plus enough for the travel to z-1. Using the same method, this requires five trips minimum. We're limited by that 180 fuel capacity, remember, so the further back we go, the shorter will be the distances and the more numerous will be the trips between fuel dumps. Hence, the distance to Dump z-2 is 180/5 = 36 km. See the pattern yet? Working backwards, we've traveled 180*1 + 60*3 + 36*5... The method of solution was the real puzzle, not the actual answer.
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Teaser 15
If there are fifteen crows on a fence and the farmer shoots a third of them, how
many are left?
(source: Carmen Green, 9th grader living in Arizona)scroll down for answer!
The Answer!
Zero crows are left. The crows all flew away when they heard the farmer shooting his gun.Teaser 16
Four blindfolded girls were each given an identical box, containing
different colored balls. One contained 3 black balls; one contained
2 black balls and 1 white ball; one contained 1 black ball and 2
white balls; and the fourth contained 3 white balls. Each box had
a label on it reading "Three Black" or "Two Black, One White" or
"One Black, Two White" or "Three White." The girls were told that
none of the four labels correctly discribed the contents of the box
to which it was attached. Each girl was told, in turn, to draw
2 balls from her box, at which point her blindfold was removed
so that she could see the 2 balls in her hand and the label on the
box assigned to her. She was given the task of trying to guess the
color of the ball remaining in her box.
As each girl drew balls from her box, their colors were
announced for all the girls to hear; but the girls cold not see the
the labels on any other box other than their own.
The first girl, having drawn 2 black balls, announced: "I know
the color of the third ball." The second girl drew 1 white and 1 black
ball, and similarly stated: "I know the color of the third ball."
The third girl withdrew 2 white balls, looked at her label, and said:
"I can't tell the color of the third ball." Finally, the fourth girl
declared: " I don't need to remove my blindfold or any balls from
my box, and yet I know the color of all three. What's more, I know
the color of the third ball in each of your boxes as well."
The first three girls were amazed by the fourth girl's
assertion and promptly challenged her. She proceeded to indentify the
contents of each box correctly. How?scroll down for answer! The Answer!
Once a girl removed 2 balls from her box, she narrowed the possible
combinations in her box to 2. If she was able to deduce the color
of the third ball, it must have been because the label on her box
showed one of the two possible combinations, forcing the actual
contents to be the other combination- remember, all the boxes
were incorrectly labeled.
The first girl's box contained either BBB or WBB, and it's
label must have read either WBB or BBB for her to have guessed the
color of the third ball. Similarly, the second girl's box must have
contained either WBB or WBW, with it's label reading either
WBW or WBB.
The third girl's box must have contained either WWW or WBW- but
her box couldn't be labled with either of these, otherwise she, too,
would have been able to deduce the color of her third ball.
The only distribution satisfying all these conditions is:
GIRL 1 2 3 4
LABEL WBB WBW BBB
ACTUAL BBB WBB ?
The fourth girl instantly realized that her box must have been
labeled WWW; since it could not actually contained WWW, the third
girl's box must have contained that combination, leaving her (fourth
girl's) box to contain WBW.
Teaser 17
Here is a rather simple question with a "yes" or "no" answer.
It just happens to be phrased in a roundabout way, but that shouldn't
disturb you if you can find a way to reduce it to it's fundamentals.
This can be done in three steps, leading to your rephrasing the
question in such simple terms that the answer is immedeately apparent.
Now go ahead.
"If the puzzle you solved before you solved the puzzle you
solved after you solved the puzzle you solved before you
solved this one, was harder than the puzzle you solved after
you solved the puzzle you solved before you solve this one,
was the puzzle you solved before you solved this one harder than this one?"
Yes or no??
scroll down for answer!
The Answer!
(1) The one you did after the one you did before this one IS this one. In other
words: (2)"....the puzzle you solved after you solved the puzzle you solved before
you solved this one" IS this one. (3) Hence the question may be rephrased this
way: "If the puzzle you solved before this one was harder than THIS ONE, was
the puzzle you solved before this one harder than THIS ONE?" (4) The answer to
this question is obviously YES.
Teaser 18You are ill and travelling down a road to the hospital. You reach a
fork in the road and find a pair of identical twin boys standing
there. One of the twins always tells the truth and the other twin
always lies. You are allowed to direct only one question to one of
the twins, and as such you will be assured of the correct road to the
hospital. What is your question and to whom?scroll down for answer! The Answer!
You ask either of the twins "If I asked your twin which path to take to get to the hospital, which way would he tell me to go?" And then I would go in the opposite path of the one I'm told. Because:
1) If I'm talking to the truth telling twin, then he will tell me what his twin would say, which would be a lie. So the direction indicated would be wrong.
2) If I'm talking to the lying twin, then he would lie about what his twin would say, which would be the truth. So the lying twin would still indicate the wrong path.
Teaser 19The owner of the local bank found a $50 bill lying in the gutter; he
picked it up and made a note of its serial number. Later that day his
wife mentioned that they owed the butcher $50, so the banker used the
bill he'd found to settle up with the butcher. The butcher used it to
pay a farmer; the farmer in turned used it to pay his feedstock
supplier; and the feedstock supplier used it to pay his laundry bill.
The laundryman used it to pay off his $50 overdraft at the local bank.
The banker recognized the bill as being the one he had found in the
gutter, but als noticed, on closer examination, that it was a fake. By
now, it had been used to settle $250 worth of debts. What was lost?scroll down for answer! The Answer!
Since the counterfeit note was used in every transaction, they are
all invalid. Therefore, everybody stands in the same position to
his/her creditor as before the banker picked up the counterfeit note.
Teaser 20The 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
a result of this series of transactions, and by whom?scroll down for answer! The Answer!
IT IS MUCH TOO HOT TO DO THESE THINGS RIGHT NOW!
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