1.

Tibetan monastery
There is a Tibetan monastery filled with a number of monks. The number of monks is more than
one, and not unreasonably large.

God visits the monks one night and tells them that he is planning on destroying the world unless
they can solve a puzzle. He puts a red dot on the foreheads of a certain number of monks, X. X is
greater than zero.

Then he takes away all means of communication between the monks, and all means by which the
monks can see themselves. No mirrors, no hand signals, no nothing. A single monk can see all
the other monks, and see if another monk has a dot on his head or no, but he cannot see himself,
and he cannot communicate in any way with any other monk.

God then says that all of the monks with dots, and only those monks with dots, must jump off of
the cliff next to the monastery and sacrifice themselves to save the world, at EXACTLY the same
moment, on EXACTLY the same day.

The next morning, all of the monks from the monastery walk out to the edge of the cliff. They
pause and look around, and then walk quickly back to the monastery.

The second morning, all of the monks from the monastery walk to the edge of the cliff. They
pause, look, and walk back to the monastery.

The third morning, all of the monks walk to the edge of the cliff. And then all of the monks with
dots, and only those monks with dots walk to the cliff edge and jump off at the exact same
moment.

The question: how many monks jumped, and how did they organize the jump?
Submitted by : George Taylor

Answer

Total 3 monks jumped in, on the third day.

There are two important points. One is that there is atleast one monk with red dot. And the
second is that all the monks are intelligent ;-)

On the day 1
If there is only one monk with red dot, he would see all monks without the red dot. So he would
know that he is the one and jump in. But no one jumped.

On the day 2
Now, all the monks know that there are atleast 2 monks with the red dots. If there are exactly two
monks with the red dot, they would see only one monk with the red dot. So they would know that
they have to jump in. But no one jumped.

On the day 3
Now, all the monks know that there are atleast 3 monks with the red dots. If there are exactly
three monks with the red dot, they would see only two monks with the red dot. So they would
know that they have to jump in.

Thus total 3 monks jumped in on the third day.

 P.S. If monks jumped in on Nth days, then there are total N monks with the red dots.

2. Army Men
There are 4 army men. They have been captured by a rebel group
and have been held at ransom. An army intelligent officer orders
them to be burried deep in dirt up to their necks. The format of their
burrial are as shown in the figure.

Conditions

• They each have hats on their heads. either black(b) or white (w) look at diagram above.
There are total 2 white hats and 2 black hats.
• They only look in front of them not behind. They are not allowed to communicate by talking.
• Between army man 1 and 2, there is a wall.
• Captive man 4 can see the colour of hats on 2 and 3
• 3 can only see 2's hat
• 2 can only see a wall and 1 can see a wall too, but is on the other side

The officer speaks up, "If one of you can correctly tell me the colour of your hat, you will all go scott
free back to your contries. If you are wrong, you will all be killed.

How can one of them be certain about the hat they are wearing and not risk the lives of their fellow
souldiers by taking a 50/50 guess!
Submitted by : KWEKU

Answer

Either soldier 3 or soldier 4 can save the life as soldier 1 and soldier 2 can not see colour of
any hat, even not their own.. In our case soldier 3 will tell the colour of his hat.

Soldier 4 can see the hat on soldier 2 and soldier 3. If both are white, then he can be sure
about colour of his hat which will be black and vice-versa. But if one of them is white and one is
black, then soldier 4 can not say anything as he can have either of them. So he will keep mum.

If soldier 4 won't say anyhing for a while, then soldier 3 will know that soldier 4 is not in position
to tell the colour of hat on his hat. It means that colour of soldier 3's hat is opposite of colour of
soldier 2's hat. So soldier 3 can tell correctly the colour of hat on his head which is Black.

Here, we are assuming that all the soldiers are intelligent enough. Also, this solution will work
for any combination of 2 Black hats and 2 White hats.

3. Cryptogram
Can you decode the following Cryptogram?

R K A P B R G S G X R R K G J N X

R K G X G X R K A Z A X R P T
 U I I Y P F I E X. R K A B A X X G S G X R

T A U F X R K G X G X R F D A.

Answer

There are two statements in the given cryptogram, both are starting with RKA. It must be
"THE". Also, there are words like RKGX and GX, which must be "THIS" and "IS" respectively.
The rest is simple substitution and application of language-knowledge to form the possible
words.
R K A P B R G S G X R R K G J N X

T H E O P T I M I S T T H I N K S

R K G X G X R K A Z A X R P T

T H I S I S T H E B E S T O F

U I I Y P F I E X. R K A B A X X G S G X R

A L L W O R L D S. T H E P E S S I M I S T

T A U F X R K G X G X R F D A.

F E A R S T H I S I S T R U E.

Brain Teaser No : 00133

Five students - Akash, Chintan, Jignesh, Mukund and Venky - appeared for an exam. There were
total five questions - two multiple choice (a, b or c) and three true/false questions. They answered
five questions each and answered as follow.

I II III IV V

--------------------------------------------------

Chintan c b True True False

Akash c c True True True

Jignesh a c False True True

Mukund b a True True False

 Venky b b True False True

--------------------------------------------------
Also, no two students got the same number of correct answers.

Can you tell which are the correct answers? What are their individual score?

Answer

The correct answers are b, a, True, False and False. Also, the scores are Jignesh (0),
Akash (1), Chintan (2), Venky (3) and Mukund (4).

As no two students got the same number of correct answers, the total number of correct
answers must be either 15 (1+2+3+4+5) or 10 (0+1+2+3+4).

Let's find out the maximum number of correct answers possible from the answers given by
them.
For Question I = 2 (b or c)
For Question II = 2 (b or c)
For Question III = 4 (True)
For Question IV = 4 (True)
For Question V = 3 (True)

Thus, the maximum number of correct answers possible are 15 (2+2+4+4+3) which means that
Akash would have given all correct answers as only he answered True for questions III, IV and
V. But then Chintan and Jignesh would have exactly 3 correct answers. And also, Mukund and
Venky would have 2 correct answers. So no one got all five correct. One can also arrive at
this conclusion by trial-and-error, but that would be bit lengthy.

Now, it is clear that total number of correct answers are 10 (0+1+2+3+4). Questions III and IV
both can not be False. If so, total number of correct answers would not be 10. So the student
who got all wrong can not be Chintan, Akash and Mukund.

If Venky got all wrong, then Chintan, Jignesh and Mukund each would have atleast 2 correct
answers. It means that Akash would have to be the student with only one correct answer and
the correct answers for questions I and II would be a and a respectively. But then the total
number of correct answers would be 1 (a) + 1 (a) + 1 (False) + 4 (True) + 2 (Flase) = 9.

Thus, Jignesh is the student with all wrong answers. The correct answers are b, a, True, False
and False. Also, the scores are Jignesh (0), Akash (1), Chintan (2), Venky (3) and Mukund (4).

Brain Teaser No : 00421

A man is at a river with a 9 gallon bucket and a 4 gallon bucket. He needs exactly 6 gallons of water.

How can he use both buckets to get exactly 6 gallons of water?

Note that he cannot estimate by dumping some of the water out of the 9 gallon bucket or the 4 gallon
bucket.
Submitted by : Andrew
 Answer

For the sack of explanation, let's identify 4 gallon bucket as Bucket P and 9 gallon bucket as
Bucket Q.
4 gallon bucket 9 gallon bucket
Operation (Bucket P) (Bucket Q)

Initially 0 0

Fill the bucket Q with 9 gallon water 0 9

Pour 4 gallon water from bucket Q to bucket P 4 5

Empty bucket P 0 5

Pour 4 gallon water from bucket Q to bucket P 4 1

Empty bucket P 0 1

Pour 1 gallon water from bucket Q to bucket P 1 0

Fill the bucket Q with 9 gallon water 1 9

Pour 3 gallon water from bucket Q to bucket P 4 6

9 gallon bucket contains 6 gallon of water, as required.

Brain Teaser No : 00061

Three friends check into a hotel for the night and the clerk tells them the bill is Rs. 30, payable in
advance. So, they each pay the clerk RS. 10 and go to their room.

A few minutes later, the clerk realizes he has made an error and overcharged the trio by Rs 5. He
asks the hotel-boy to return Rs. 5 to the 3 friends who had just checked in. The hotel-boy sees this
as an opportunity to make Rs. 2 as he reasons that the three friends would have a tough time
dividing Rs. 5 evenly among them; so he decides to tell them that the clerk made a mistake of only
Rs. 3, giving a rupee back to each of the friends. He pockets the leftover Rs. 2 and goes home for
the day!

Now, each of the three friends gets a rupee back, thus they each paid Rs. 9 for the room which is a
total of Rs. 27 for the night. We know the hotel-boy pocketed Rs. 2 and adding that to the Rs. 27,
you get Rs. 29, not Rs. 30 which was originally spent.

Where did the other rupee go???

Answer

The facts in this riddle are clear: There is an initial Rs. 30 charge. It should have been Rs. 25,
so Rs.5 must be returned and accounted for. Rs. 3 is given to the 3 friends, Rs. 2 is kept by the
hotel-boy - there you have the Rs. 5.
 The trick to this riddle is that the addition and subtraction are done at the wrong times to
misdirect your thinking - and quite successfully for most. Each of the 3 friends did indeed pay
Rs. 9, not Rs. 10, and as far as the friends are concerned, they paid Rs. 27 for the night. But
we know that the clerk will tell us that they were charged only Rs. 25 and when you add the Rs.
3 returned with the Rs. 2 kept by the hotel-boy, you come up with Rs. 30

Brain Teaser No : 00105

A man is on a search for Atlantis and comes upon an island where all the inhabitants know whether
Atlantis is still around or not.

However, all of the inhabitants are either Fairies or Trolls and they all use a spell to appear
humanoid so you cannot tell which is which. And the Faries always tell the truth and the Trolls
always lie, but there is a slight complication, some of the Fairies have gone insane and always lie
and some of the Trolls have also gone insane and always tell the truth.

So here is your task: you must ask the first inhabitant that you come to ONE question and from that
ONE question you must determine wether Atlantis is still around or not.

What is the question that you must ask?

Answer

There are 2 answers to it:

Answer I"Is the statement that you are reliable equivalent to the statement that Atlantis is still
around?"

Answer II"Do you believe that the Statement that you are a Fairy is equivalent to the statement
that Atlantis is still around?"

Brain Teaser No : 00173

Tom and Jerry and the boys in the bar were exchanging old war stories.

Tom offered one about how his grandfather led a battalion against a German division during World
War I. Through brilliant maneuvers, he defeated them and captured valuable territory. After the battle
he was awarded a medal that was inscribed with:

"For Bravery, Daring and Leadership - World War I.

From the Men of Battalion 8."

Jerry looked at Tom and said, "You really don't expect anyone to believe that yarn, do you?"

What's wrong with the story?

Answer
 World War I wasn't called "World War I" until World War II.

Brain Teaser No : 00527

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 the safest for him?

Submitted by : Helen Normandin

Answer

The third room - full of lions - is the safest.

The third room is full of lions that HAVEN'T EATEN IN 3 YEARS. It is obvious that they won't
survive without eating for 3 years, they must be dead.

Brain Teaser No : 00215

Sam and Mala have a conversation.

• Sam says I am certainly not over 40

• Mala says I am 38 and you are atleast 5 years older than me
• Now Sam says you are atleast 39

All the statements by the two are false. How old are they really?

Answer

Sam is 41 and Mala is 37.

Let's invert the teaser and read it like this :

• Sam says I am certainly over 40

• Mala says I am not 38 and you are atmost 4 years older than me
• Now Sam says you are atmost 38

From first statement it is clear that Sam is over 40. Also, from next 2 statements it is clear that
Mala is less then 38. Hence the possibilities are :
Sam = 41, 42, 43, 44, 45, ......
Mala = 37, 36, 35, 34, 33, ......

It also says that the difference between their age is maximum 4 years. Hence, there is only one
possible pair i.e. 41 and 37, all other combination have differences more then 4.

Hence the answer - Sam is 41 and Mala is 37.

Brain Teaser No : 00028

There are 10 boxes containing 10 balls each. 9 boxes contain 10 balls of 10 kg each and one box
contains 10 balls of 9 kg each. Tool is available for proper weighing. How can you find out the box
containing 9 kg balls?

You are allowed to weigh only once. You can remove balls from the boxes. All balls are of same size
and color.

Answer

1. Mark the boxes with numbers 1, 2, 3, 4, ... upto 10

2. Take 1 ball from box 1, take 2 balls from box 2, take 3 balls from box 3, take 4 balls
from box 4 and so on
3. Put all of them on the scale at once and take the measurement.
4. Now, subtract the measurement from 550 ( 1*10 + 2*10 + 3*10 + 4*10 + 5*10 + 6*10 +
7*10 + 8*10 + 9*10 + 10*10)

5. The result will give you the box number which has a ball of 9 Kg

Brain Teaser No : 00033

There are 9 coins. Out of which one is odd one i.e weight is less or more. How many iterations of
weighing are required to find odd coin?

Answer

It is always possible to find odd coin in 3 weighings and to tell whether the odd coin is heavier
or lighter.

1. Take 8 coins and weigh 4 against 4.

o If both are not equal, goto step 2
o If both are equal, goto step 3

2. One of these 8 coins is the odd one. Name the coins on heavier side of the scale as
H1, H2, H3 and H4. Similarly, name the coins on the lighter side of the scale as L1, L2,
L3 and L4. Either one of H's is heavier or one of L's is lighter. Weigh (H1, H2, L1)
against (H3, H4, X) where X is one coin remaining in intial weighing.

o If both are equal, one of L2, L3, L4 is lighter. Weigh L2 against L3.
 If both are equal, L4 is the odd coin and is lighter.
 If L2 is light, L2 is the odd coin and is lighter.
 If L3 is light, L3 is the odd coin and is lighter.

o If (H1, H2, L1) is heavier side on the scale, either H1 or H2 is heavier. Weight
H1 against H2
  If both are equal, there is some error.
 If H1 is heavy, H1 is the odd coin and is heavier.
 If H2 is heavy, H2 is the odd coin and is heavier.

o If (H3, H4, X) is heavier side on the scale, either H3 or H4 is heavier or L1 is

lighter. Weight H3 against H4
 If both are equal, L1 is the odd coin and is lighter.
 If H3 is heavy, H3 is the odd coin and is heavier.
 If H4 is heavy, H4 is the odd coin and is heavier.

3. The remaining coin X is the odd one. Weigh X against the anyone coin used in initial
weighing.
o If both are equal, there is some error.
o If X is heavy, X is the odd coin and is heavier.

o If X is light, X is the odd coin and is lighter.

Brain Teaser No : 00092

Below is a Quiz written by Einstein in the lst century.

He said 98% of the people in the world cannot solve the quiz. Are you among the other 2%?
FACTS

1. There are 5 houses in 5 different colors.

2. In each house lives a person with a different nationality.
3. These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain
pet.
4. No owners have the same pet, smoke the same brand of cigar or drink the same drink.

HINTS

1. The Brit lives in a red house.

2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The green house is on the immediate left of the white house.
5. The green house owner drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the yellow house smokes Dunhill.
8. The man living in the house right in the center drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes blend lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The owner who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the Blue House.
 15. The man who smokes blend has a neighbor who drinks water.

THE QUESTION IS....WHO KEEPS FISH?

There is no trick to this - it needs deductive reasoning and definitely a pen and paper.

Answer

Nationality Beverage Cigar Pet House Color

------------------------------------------------------

Norwegian Water Dunhill Cat Yellow

Dane Tea Blend Horses Blue

Brit Milk Pall Mall Bird Red

German Coffee Prince Fish Green

Swede Beer Blue Master Dog White

Therefore the answer is the German.

I wonder if U could work it out by realizing that Einstien was a german and kept fish but that
would probably be cheating :)

There is one more possible answer, if we remove "immediate" from the Hint 4 i.e. read it as
"The green house is on the left of the white house, not necessarily on the immediate left"
Nationality Beverage Cigar Pet House Color

------------------------------------------------------

Norwegian Coffee Blend Fish Green

German Water Prince Cats Blue

Swede Milk Dunhill Dogs Yellow

Brit Beer Blue Master Horses Red

Dane Tea Pall Mall Birds White

Thus, either German or Norwegian keeps the Fish, if the green house is not necessarily on the
immediate left of the white house.

Thanks to Katie Crowe and friends for the second answer !!!

Brain Teaser No : 00223

A professor went to a Museum of Natural History. She saw the following five exhibits :

1. A prehistoric arrowhead made of copper.

2. The fossil skeleton of a dinosaur no bigger than a chicken.
3. An ancient Roman coin marked 120 B.C.
 4. A red diamond ring.
5. An ancient Egyptian cat mummy.

The professor knew one of these is fake. Do you?

Submitted by : Kimi

Answer

An ancient Roman coin marked 120 B.C. is fake.

B.C. stands for "Before Christ". The ancient Roman people did not know that they were before
Christ. or what B.C. stands for. Infact nobody would have knew that they were 120 years
before Christ !!!

Brain Teaser No : 00468

A blindfolded man is asked to sit in the front of a carrom board. The holes of the board are shut with
lids in random order, i.e. any number of all the four holes can be shut or open.

Now the man is supposed to touch any two holes at a time and can do the following.

• Open the closed hole.

• Close the open hole.
• Let the hole be as it is.

After he has done it, the carrom board is rotated and again brought to some position. The man is
again not aware of what are the holes which are open or closed.

How many minimum number of turns does the blindfolded man require to either open all the holes or
close all the holes?

Note that whenever all the holes are either open or close, there will be an alarm so that the
blindfolded man will know that he has won.
Submitted by : Vikrant Ramteke

Answer

The blindfolded man requires 5 turns.

1. Open two adjacent holes.

2. Open two diagonal holes. Now atleast 3 holes are open. If 4th hole is also open, then
you are done. If not, the 4th hole is close.

3. Check two diagonal holes.

o If one is close, open it and all the holes are open.
o If both are close, open any one hole. Now, two holes are open and two are
close. The diagonal holes are in the opposite status i.e. in both the diagonals,
one hole is open and one is close.
 4. Check any two adjacent holes.
o If both are open, close both of them. Now, all holes are close.
o If both are close, open both of them. Now, all holes are open.
o If one is open and one is close, invert them i.e. close the open hole and open
the close hole. Now, the diagonal holes are in the same status i.e. two holes in
one diagonal are open and in other are close.

5. Check any two diagonal holes.

o If both are open, close both of them. Now, all holes are close.

o If both are close, open both of them. Now, all holes are open.

Brain Teaser No : 00258

Three convicts are brought into the warden's office. He says he can parole on of them and to
decide which one he will parole he takes out 5 hats (3 red and 2 white). He stands behind them
and places a hat on each one of their heads and puts the other two remaining hats in a drawer.

He tells the prisioners they can look at the others hats and if they can tell which hat they have on
they will be the one who is paroled.

The first man looks at the other two and says, "I don't know."

The second man looks at the others hats and says, "I don't know."

The third man who is blind says, "Even though I have not the gift of sight I can tell by what the
others have said that the color of my hat is..."

What color is the blind mans hat and how does he know?
Submitted by : Anne Hanna

Answer

The color of blind man's hat is Red.

It is sure that the first man saw either both Red hats or one White hat and one Red hat. There are
6 such possibilities:
 1) R R R

2) R R W

3) R W R

4) W R R

5) W R W

6) W W R
In all above possibilities, the first man won't be sure of the color of his hat.

Now, the second man knows that the first man saw either both Red hats or one White hat and
one Red hat. And, he also knows that its one of the above 6 possibilities. (like we know ;)) But he
says, "I don't know". That means that (2) and (5) are not the possibilities as in either case he
would be sure of the color of his hat (Red) by just looking at the third man's color of hat (White).

Now, the blind man knows that there are just 4 possibilities - (1), (3), (4), (6) - and in all, the color
of his hat is Red.

Brain Teaser No : 00043

Professors Ahmad and Joshi are extremely strange persons.

Prof. Ahmad lies on Mondays, Tuesdays and Wednesdays, but tells true on other days of the
week.

Prof. Joshi lies on Thursdays, Fridays and Saturdays, but tells true on other days of the week.

• They made the following statements:

Prof. Ahmad : "Yesterday was one of my lying days."
Prof. Joshi : "Yesterday was one of my lying days too."
What day of the week was it?

• Both Professors looked very alike and one day they said to a visitor to their department :
First Prof: "I'm Ahmed."
Second Prof: "I'm Joshi."
Who was who? What day of the week was it?

• On another occasion, both Professors made the following statements:

First Prof : 1. "I lie on Saturdays."
2. "I lie on Sundays."
Second Prof. : "I will lie tomorrow."
What day of the week was it?

Answer

Mon Prof. Ahmad Prof. Joshi

Lies tells truth
 Lies Tells truth

Tue

Wed Lies Tells truth

Thu Tells truth Lies

Fri Tells truth Lies

Sat Tells truth Lies

Sun Tells truth Tells truth

Teaser 1 :
Assume that Prof. Ahmad is telling truth => today is Thursday
Assume that Prof. Ahmad is lying => today is Monday
Similarly, Assume Prof. Joshi is telling truth => today is Sunday
Assume that Prof. Joshi is lying => today is Thrusday.
Hence, today is Thrusday, Prof. Ahmad is telling truth and Prof. Joshi is lying.

Teaser 2 :
Assume that First Prof. is telling truth => Thursday, Friday, Saturday or Sunday
Assume that First Prof. is lying => Thursday, Friday or Saturday
Similarly, Assume Second Prof. is telling truth => Monday, Tuesday, Wednesday or Sunday
Assume that Second Prof. is lying => Monday, Tuesday, Wednesday
The only possibility is Sunday and both are telling truth.

Teaser 3 :
A simple one. First Prof. says - "I lie on Sunday" which is false as both the Prof. tell truth on
sunday. It means the first statement made by the First Prof. is also false. It means the First Prof.
tells truth on Saturday. Hence First Prof. is Prof. Ahmad and he is lying. It means that today is
either Monday, Tuesday or Wednesday.

It is clear that Second Prof. is Prof. Joshi.

Assume that he is telling truth => today is Wednesday
Assume that he is lying => today is Saturday.

Hence, today is Wednesday !!!

Brain Teaser No : 00580

In Column-I below, are given some words. These have been translated into a code language. The
code equivalents of the words in Column-I are given in Column-II, not necessarily opposite to the
corresponding words. Also, the codes for the different letters in each word have also not been given
the same order as these letter occur in the original word.

COLUMN-I COLUMN-II

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

TAPE moi

COP lhhpok

TIE nls

ROTATE nhpk

SAY nkpl

TREAT msr

YEAR khlph

SIP hrp

TYRE pmlh
Can you decode the individual letter codes?

Answer

We first find the exact codes of the each given words.

ROTATE is a 6-letter word. So its code is lhhpok. And h is for T.

TREAT is a 5-letter word. So its code is khlph.

The 4-letter words are TAPE, YEAR, TYRE and codes are nhpk, nkpl, pmlh. YEAR and TYRE
have 3 letters in common (Y, E, R). They must be either nhpk or nkpl. Hence, the code for
TAPE is pmlh and m is for P. Also the code for TYRE is nhpk (as h is for T) and the code for
YEAR is nkpl.

The 3-letter words are COP, TIE, SAY, SIP and codes are moi, nls, msr, hrp.
The code for TIE is hrp.
The code for SIP is msr.
The code for COP is moi. And the code for SAY is nls.

Thus, the words and their codes are:

ROTATE lhhpok

TREAT khlph

TAPE pmlh

TYRE nhpk

YEAR nkpl
 TIE hrp

COP moi

SIP msr

SAY nls
So far we know that h is for T and m is for P.

In SAY and SIP, the common letter is S stands for s.

In TYRE and SAY, the common letter Y stands for n.
Thus, in SAY, the remaining letter A stands for l.

In TIE and SIP, the common letter I stands for r.

Thus, in TIE, the remaining letter E stands for p.

In ROTATE and COP, the common letter O stands for o.

Thus, in ROTATE, the remaining letter R stands for k.
Also, in COP, the remaining letter C stands for i.

Summerizing h-T, i-C, k-R, l-A, m-P, n-Y, o-O, p-E, r-I, s-S

Brain Teaser No : 00139

There was a man who had just hung himself. When you search the room where it happend all you
can see is the young man hanging and a puddle of water below him. There are no objects or
furniture that could have helped him to commit suicide.

How did he kill himself?

Submitted by : beka chesse

Answer

The man stood on a block of ice. When it melted, he hung himself or he jumped off and hung
himself.

Brain Teaser No : 00060

A woman had two sons who were born on the same hour of the same day of the same month of the
same year. But they were not twins.

How could this be so?

Answer

This is a lateral thinking puzzle.

They were two of a set of triplets (or quadruplets, etc.).

This puzzle stumps many people. They try outlandish solutions involving test-tube babies or
surrogate mothers. Why does the brain search for complex solutions when there is a much
 simpler one available?

Brain Teaser No : 00069

A woman goes into a hardware store to buy something for her house. When asked the price, the
clerk replies, "the price of one is twelve cents, the price of forty-four is twenty-four cents, and the
price a hundred and forty-four is thirty-six cents.

What does the woman want to buy?

Answer

House numbers.

Price of one i.e. 1 = 12 cents (as only number 1)

Price of forty-four i.e. 44 = 24 cents (as there are two numbers)
Price of a hundred and forty-four i.e. 144 = 36 cents (as there are three numbers)

Brain Teaser No : 00056

A man is wearing black. Black shoes, socks, trousers, jumper, gloves and balaclava. He is walking
down a black street with all the street lamps off. A black car is coming towards him with its light off
but somehow manages to stop in time.

How did the driver see the man?

Answer

This is a lateral thinking puzzle.

It was day time.

Brain Teaser No : 00104

A farmer needs 8 gallons of water. He has only three unmared buckets, two 6 gallon and one 11
gallon bucket.

How can he collect 8 gallons of water using three unmarked buckets? Provide solution with minimal
water wastage.
 Answer

Here is the solution with 10 gallon water wastage.

OPERATIONS 6 6 11
Fill 6 gallon bucket with water 6 0 0
Empty 6 gallon bucket into 11 gallon bucket 0 0 6
Fill 6 gallon bucket with water 6 0 6
Fill 11 gallon bucket to full using filled 6 gallon bucket. This will leave 1 gallon water
1 0 11
in 6 gallon bucket
Empty 11 gallon bucket into second 6 gallon bucket. 1 6 5
Empty 11 gallon bucket - wastage of 5 gallon water 1 6 0
Empty second 6 gallon bucket into 11 gallon bucket 1 0 6
Fill seccond 6 gallon bucket with water 1 6 6
Fill 11 gallon bucket to full using filled second 6 gallon bucket. This will leave 1
1 1 11
gallon water in second 6 gallon bucket
Fill first 6 gallon bucket with 1 gallon water which is in second 6 gallon bucket 2 0 11
Empty 11 gallon bucket into second 6 gallon bucket. 2 6 5
Empty 11 gallon bucket - wastage of 5 gallon water 2 6 0
Fill 11 gallon bucket with water in both the 6 gallon buckets 0 0 11

Brain Teaser No : 00221

An electric train is going south but the wind is blowing westward.

Which direction will the smoke from the train be blowing?

Submitted by : Hannah Brooks

Answer

It is an Electric Train. And Electric trains do not produce any smoke. Therefore there is no
smoke to be blown

Brain Teaser No : 00099

You have someone working for you for seven days and a gold bar to pay them. The gold bar is
segmented into seven connected pieces. You must give them a piece of gold at the end of every
day.

If you are only allowed to make two breaks in the gold bar, how do you pay your worker?

Answer
 Make two breaks such that you get three segments with 1 piece, 2 pieces and 4 pieces and
follow as below:

Day 1 : Give a single segment to the worker.

Day 2 : Ask the worker to return the segment you gave him on day 1 and give him the segment
with Two connected pieces.
Day 3 : GIve the worker the 1 piece segment you have.
Day 4 : Ask the worker to return all pieces he has (one segment and 2 segment pieces) and
give him the segment with 4 pieces on it.
Day 5 : Give him the the segment with 1 piece.
Day 6 : Ask him to return the 1 piece segment and give him the segment with two pieces.
Day 7 : Give him the 1 piece segment you have.

Brain Teaser No : 00084

You are in a room with 2 doors leading out. Behind 1 door is a coffer overflowing with jewels & gold,
along with an exit. Behind the other door is an enormous, hungry lion that will pounce on anyone
opening the door. You do not know which door leads to the treasure & exit, & which door leads to
the lion.

In the room you are in, are 2 individuals. The first is a knight, who always tells the truth, & a knave,
who always lies. Both of these individuals know what is behind each door. You do not know which
individual is the knight, or which one is the knave.

You may ask 1 of the individuals exactly 1 question. What should you ask in order to be certain that
you will open the door with the coffer behind it, instead of the hungry lion?

Answer

There are 2 possible answers for this puzzle:

Answer 1: You ask one of the individuals what the other one would say if you asked him or her
which door you should open to get to the coffer. In this case, you would open the other door.

Answer 2: You ask one of the individuals what the other one would say if you asked him or her
which door is holding back the hungry lion. In this case, you would open this door.

Brain Teaser No : 00289

You have 13 balls which all look identical. All the balls are the same weight except for one. Using
only a balance scale, can find the odd one out with only 3 weighings?

Is it possible to always tell if the odd one out is heavier or lighter than the other balls?
Submitted by : Brett Hurrell

Answer

It is always possible to find odd ball in 3 weighings and in most of the cases it is possible to tell
whether the odd ball is heavier or lighter. Only in one case, it is not possible to tell the odd ball
is whether heavier or lighter.
1. Take 8 balls and weigh 4 against 4.
o If both are not equal, goto step 2
o If both are equal, goto step 3

2. One of these 8 balls is the odd one. Name the balls on heavier side of the scale as H1,
H2, H3 and H4. Similarly, name the balls on the lighter side of the scale as L1, L2, L3
and L4. Either one of H's is heavier or one of L's is lighter. Weigh (H1, H2, L1) against
(H3, H4, X) where X is one ball from the remaining 5 balls in intial weighing.

o If both are equal, one of L2, L3, L4 is lighter. Weigh L2 against L3.
 If both are equal, L4 is the odd ball and is lighter.
 If L2 is light, L2 is the odd ball and is lighter.
 If L3 is light, L3 is the odd ball and is lighter.

o If (H1, H2, L1) is heavier side on the scale, either H1 or H2 is heavier. Weight
H1 against H2
 If both are equal, there is some error.
 If H1 is heavy, H1 is the odd ball and is heavier.
 If H2 is heavy, H2 is the odd ball and is heavier.

o If (H3, H4, X) is heavier side on the scale, either H3 or H4 is heavier or L1 is

lighter. Weight H3 against H4
 If both are equal, L1 is the odd ball and is lighter.
 If H3 is heavy, H3 is the odd ball and is heavier.
 If H4 is heavy, H4 is the odd ball and is heavier.

3. One of the remaining 5 balls is the odd one. Name the balls as C1, C2, C3, C4, C5.
Weight (C1, C2, C3) against (X1, X2, X3) where X1, X2, X3 are any three balls from
the first weighing of 8 balls.

o If both are equal, one of remaining 2 balls is the odd i.e. either C4 or C5.
Weigh C4 with X1
 If both are equal, C5 is the odd ball. But you can not tell whether it is
heavier or lighter.
 If C4 is heavy, C4 is the odd ball and is heavier.
 If C4 is light, C4 is the odd ball and is lighter.

o If (C1, C2, C3) is heavier side, one of C1, C2, C3 is the odd ball and is
heavier. Weigh C1 and C2.
  If both are equal, C3 is the odd ball and is heavier.
 If C1 is heavy, C1 is the odd ball and is heavier.
 If C2 is heavy, C2 is the odd ball and is heavier.

o If (C1, C2, C3) is lighter side, one of C1, C2, C3 is the odd ball and is lighter.
Weigh C1 and C2.
 If both are equal, C3 is the odd ball and is heavier.
 If C1 is light, C1 is the odd ball and is lighter.

 If C2 is light, C2 is the odd ball and is lighter.

Brain Teaser No : 00558

There are four people in a room (not including you). Exactly two of these four always tell the truth.
The other two always lie.

You have to figure out who is who IN ONLY 2 QUESTIONS. Your questions have to be YES or NO
questions and can only be answered by one person. (If you ask the same question to two different
people then that counts as two questions). Keep in mind that all four know each other's
characteristics whether they lie or not.

What questions would you ask to figure out who is who? Remember that you can ask only 2
questions.
Submitted by : Ryan Hutcherson

Answer

0-represents a Liar
1-represents a Truth Teller
A B C D

-------

0 0 1 1 A and B are Liars

0 1 0 1 A and C are Liars

0 1 1 0 A and D are Liars

1 0 0 1 B and C are Liars

1 0 1 0 B and D are Liars

1 1 0 0 C and D are Liars

As you can see there are 6 possible cases. If you give only yes or no questions and get only
yes or no responses the best you can do is eliminate half of the cases for every question
asked. That means after asking the first question the best (worst case) scenario you can end
up with is to eliminate all but three cases. That means that the next question addresses three
cases and can at best eliminate only 1!

That means that you cannot solve this in 2 questions "giving only yes or no questions and get
ONLY yes or no responses". The trick is to ask a question that has the potential of being
answered with: "yes", "no", or no response at all.

First Question
Ask A: is B a Truth teller AND is C a Liar.
(Asking A: does B=1 AND does C=0)

if answer to first Question is YES: then do {PART 1}

if answer to first Question is NO: then skip to {PART 2}

---------------------{PART 1}---------------------
we know it is one of the following scenarios:
A B C D

-------

0 0 1 1

1 1 0 0

0 1 1 0

Second Question:
Ask C: Let's assign a value of 0 for every Liar and a value of 1 for every Truth teller in
the room. Let's also suppose that B has a secret number in his head that ONLY HE
KNOWS. All we know about this number is that it is greater than 0, less than 2, and is
not an integer. Would B say that the sum of A and B is greater than the secret number
he is thinking of?
(Asking C: would B say (A+B) > n; where 0>n>2 and n is not an integer)
If C answers YES:

A B C D

-------

0 0 1 1 A and B are the Liars

If A and B are Liars then their sum (0+0) will 0. We know the number B is thinking of is greater
than 0. Therefore B will lie and say YES. C will tell us the truth of what B would say and so he
says YES.
If C answers NO:

A B C D

-------

1 1 0 0 C and D are the Liars

If A and B are Truth tellers then their sum (1+1) will 2. We know the number B is thinking of is
less than 2. Therefore B will tell the truth and say YES. HOWEVER, C will LIE about what B
will say and his response will be NO.
IF C DOESN'T answer:

A B C D

-------

0 1 1 0 A and D are the Liars

If A is a liar and B is a Truth teller then their sum (0+1) will 1. We know the number B is
thinking of is less than 2 and greater than 0 but ONLY B KNOWS for sure what its value is.
Therefore C does not know for sure what B will say (even though he knows it will be the truth).
Therefore C doesn't answer because if he did he could run the risk of telling a lie which, of
course, he never does. [ALL DONE]

---------------------{PART 2}---------------------
We know it is one of the following scenarios:
A B C D

-------

1 0 0 1

1 0 1 0

0 1 0 1

Second Question:
Ask C: Let's assign a value of 0 for every Liar and a value of 1 for every Truth teller in
the room. Let's also suppose that B has a secret number in his head that ONLY HE
KNOWS. All we know about this number is that it is greater than 0, less than 2, and is
not an integer. Would B say that the sum of D and B is greater than the secret number
he is thinking of?
(Asking C: would B say (D+B) > n; where 0>n>2 and n is not an integer)
If C answers YES:

A B C D

-------

1 0 1 0 B and D are the Liars

If D and B are Liars then their sum (0+0) will 0. We know the number B is thinking of is greater
than 0. Therefore B will lie and say YES. C will tell us the truth of what B would say and so he
says YES.
If C answers NO:

A B C D

-------

0 1 0 1 A and C are the Liars

If D and B are Truth tellers then their sum (1+1) will 2. We know the number B is thinking of is
less than 2. Therefore B will tell the truth and say YES. HOWEVER, C will LIE about what B
will say and his response will be NO.
IF C DOESN'T answer:

A B C D

-------

1 0 0 1 B and C are the Liars

If B is a liar and D is a Truth teller then their sum (0+1) will 1. We know the number B is
thinking of is less than 2 and greater than 0 but ONLY B KNOWS for sure what its value is.
Therefore C does not know for sure what B will say (even though he knows it will be a lie).
Therefore C doesn't answer because if he did he could run the risk of telling the truth which, of
course, he never does. [ALL DONE]

Thanks to Ryan Hutcherson !!!

Here is one more valid answer (and much more simpler) from Carmel.

Lets call our people A, B, C & D

T = always tells the truth

L = always lies

"Same" means both liars or both truthtellers.

"Different" means one is a liar and one tells the truth.
Ask D "IF A AND B ARE DIFFERENT, is A a truth-teller?"

If D answers yes,

Ask A "Are B and C the same?"

If A answers yes

A=T, B=L, C=L, D=T

If A answers no

A=L, B=T, C=T, D=L

If D answers no,

Ask A "Are B and D the same?"

 If A answers yes

A=T, B=L, C=T, D=L

If A answers no

A=L, B=T, C=L, D=T

If D doesn't answer, then it means that

A and B are the same.

Ask A "Are C & D the same?"

If A answers yes,

A=T, B=T, C=L, D=L

If A answers no,

A=L, B=L, C=T, D=T

Explanation: there are six different outcomes, you only get 2 questions. The questions can only
be answered yes or no. There is no stipulation that anyone MUST answer a question.

Brain Teaser No : 00105

A man is on a search for Atlantis and comes upon an island where all the inhabitants know whether
Atlantis is still around or not.

However, all of the inhabitants are either Fairies or Trolls and they all use a spell to appear
humanoid so you cannot tell which is which. And the Faries always tell the truth and the Trolls
always lie, but there is a slight complication, some of the Fairies have gone insane and always lie
and some of the Trolls have also gone insane and always tell the truth.

So here is your task: you must ask the first inhabitant that you come to ONE question and from that
ONE question you must determine wether Atlantis is still around or not.

What is the question that you must ask?

Answer
 There are 2 answers to it:

Answer I"Is the statement that you are reliable equivalent to the statement that Atlantis is still
around?"

Answer II"Do you believe that the Statement that you are a Fairy is equivalent to the statement
that Atlantis is still around?"

Brain Teaser No : 00450

Yesterday in a party, I asked Mr. Shah his birthday. With a mischievous glint in his eyes he replied.
"The day before yesterday I was 83 years old and next year I will be 86."

Can you figure out what is the Date of Birth of Mr. Shah? Assume that the current year is 2000.

Answer

Mr. Shah's date of birth is 31 December, 1915

Today is 1 January, 2000. The day before yesterday was 30 December, 1999 and Mr. Shah
was 83 on that day. Today i.e. 1 January, 2000 - he is 84. On 31 December 2000, he will be 85
and next year i.e. 31 December, 2001 - he will be 86. Hence, the date of birth is 31 December,
1915.

Many people do think of Leap year and date of birth as 29th February as 2000 is the Leap year
and there is difference of 3 years in Mr. Shah's age. But that is not the answer.

Brain Teaser No : 00057

One day Kerry celebrated her birthday. Two days later her older twin brother, Terry, celebrated his
birthday.

How? Note that they both celebrated their birthday on their actual birthdays.

Answer

This is a lateral thinking puzzle.

At the time she went into labor, the mother of the twins was traveling by boat. The older twin,
Terry, was born first early on March 1st. The boat then crossed a time zone and Kerry, the
younger twin, was born on February the 28th. Therefore, the younger twin celebrates her
birthday two days before her older brother.

There is one more answer submitted by Beano.

She obviously had an older set of twin brothers and their birthday was 2 days after hers, they
just didn't mention that it was also her other twin brothers birthday.

Also, according to Robbie TWINS DONT HAVE TO HAVE THE SAME BIRTHDAY! SOME
TWINS ARE BORN 300 DAYS APART !!!

Brain Teaser No : 00011

When Alexander the Great attacked the forces of Porus, an Indian soldier was captured by the
Greeks. He had displayed such bravery in battle, however, that the enemy offered to let him choose
how he wanted to be killed. They told him, "If you tell a lie, you will put to the sword, and if you tell
the truth you will be hanged."

The soldier could make only one statement. He made that statement and went free. What did he
say?

Answer

The soldier said, "You will put me to the sword."

The soldier has to say a Paradox to save himself. If his statement is true, he will be hanged,
which is not the sword and hence false. If his statement is false, he will be put to the sword,
which will make it true. A Paradox !!!

Brain Teaser No : 00800

There are 4 mathematicians - Brahma, Sachin, Prashant and Nakul - having lunch in a hotel.
Suddenly, Brahma thinks of 2 integer numbers greater than 1 and says, "The sum of the numbers
is..." and he whispers the sum to Sachin. Then he says, "The product of the numbers is..." and he
whispers the product to Prashant. After that following conversation takes place :

Sachin : Prashant, I don't think that we know the numbers.

Prashant : Aha!, now I know the numbers.
Sachin : Oh, now I also know the numbers.
Nakul : Now, I also know the numbers.

What are the numbers? Explain your answer.

Submitted by : Sachin Kanekar

Answer

The numbers are 4 and 13.

As Sachin is initially confident that they (i.e. he and Prashant) don't know the numbers, we can
conclude that -
1) The sum must not be expressible as sum of two primes, otherwise Sachin could not have
been sure in advance that Prashant did not know the numbers.
2) The product cannot be less than 12, otherwise there would only be one choice and Prashant
would have figured that out also.

Such possible sum are - 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79,
83, 87, 89, 93, 95, 97, 101, 107, 113, 117, 119, 121, 123, 125, 127, 131, 135, 137, 143, 145,
147, 149, 155, 157, 161, 163, 167, 171, 173, 177, 179, 185, 187, 189, 191, 197, ....

Let's examine them one by one.

If the sum of two numbers is 11, Sachin will think that the numbers would be (2,9), (3,8), (4,7)
or (5,6).
Sachin : "As 11 is not expressible as sum of two primes, Prashant can't know the numbers."

Here, the product would be 18(2*9), 24(3*8), 28(4*7) or 30(5*6). In all the cases except for
product 30, Prashant would know the numbers.

- if product of two numbers is 18:

Prashant : "Since the product is 18, the sum could be either 11(2,9) or 9(3,6). But if the sum
was 9, Sachin would have deduced that I might know the numbers as (2,7) is the possible
prime numbers pair. Hence, the numbers must be 2 and 9." (OR in otherwords, 9 is not in the
Possible Sum List)

- if product of two numbers is 24:

Prashant : "Since the product is 24, the sum could be either 14(2,12), 11(3,8) or 10(4,6). But
14 and 10 are not in the Possible Sum List. Hence, the numbers must be 3 and 8."

- if product of two numbers is 28:

Prashant : "Since the product is 28, the sum could be either 16(2,14) or 11(4,7). But 16 is not
in the Possible Sum List. Hence, the numbers must be 4 and 7."

- if product of two numbers is 30:

Prashant : "Since the product is 30, the sum could be either 17(2,15), 13(3,10) or 11(5,6). But
13 is not in the Possible Sum List. Hence, the numbers must be either (2,15) or (5,6)." Here,
Prashant won't be sure of the numbers.

Hence, Prashant will be sure of the numbers if product is either 18, 24 or 28.

Sachin : "Since Prashant knows the numbers, they must be either (3,8), (4,7) or (5,6)." But he
won't be sure. Hence, the sum is not 11.

Summerising data for sum 11:

Possible Sum PRODUCT Possible Sum
2+9 18 2+9=11 (possible)
3+6=9
3+8 24 2+12=14
3+8=11 (possible)
4+6=10
4+7 28 2+12=14
3+8=11 (possible)
4+6=10
5+6 30 2+15=17 (possible)
3+10=13
5+6=11 (possible)

Following the same procedure for 17:

Possible Sum PRODUCT Possible Sum
2+15 30 2+15=17 (possible)
3+10= 13
 5+6=11 (possible)
3+14 42 2+21=23 (possible)
3+14=17 (possible)
6+7=13
4+13 52 2+26=28
4+13=17 (possible)
5+12 60 2+30=32
3+20=23 (possible)
4+15=19
5+12=17 (possible)
6+10=16
6+11 66 2+33=35 (possible)
3+22=25
6+11=17 (possible)
7+10 70 2+35=37 (possible)
5+14=19
7+10=17 (possible)
8+9 72 2+36=38
3+24=27 (possible)
4+18=22
6+12=18
8+9=17 (possible)

Here, Prashant will be sure of the numbers if the product is 52.

Sachin : "Since Prashant knows the numbers, they must be (4,13)."

For all other numbers in the Possible Sum List, Prashant might be sure of the numbers but
Sachin won't.

Here is the step by step explaination:

Sachin : "As the sum is 17, two numbers can be either (2,15), (3,14), (4,13), (5,12), (6,11),
(7,10) or (8,9). Also, as none of them is a prime numbers pair, Prashant won't be knowing
numbers either."

Prashant : "Since Sachin is sure that both of us don't know the numbers, the sum must be one
of the Possible Sum List. Further, as the product is 52, two numbers can be either (2,26) or
(4,13). But if they were (2,26), Sachin would not have been sure in advance that I don't know
the numbers as 28 (2+26) is not in the Possible Sum List. Hence, two numbers are 4 and 13."

Sachin : "As Prashant now knows both the numbers, out of all possible products - 30(2,15),
42(3,14), 52(4,13), 60(5,12), 66(6,11), 70(7,10), 72(8,9) - there is one product for which list of
all possible sum contains ONLY ONE sum from the Possible Sum List. And also, no such two
lists exist. [see table above for 17] Hence, two numbers are 4 and 13."

Nakul figured out both the numbers just as we did by observing the conversation between
Sachin and Prashant.
 It is interesting to note that there are no other such two numbers. We checked all the possible
sums till 500 !!!

Brain Teaser No : 00417

Decipher this sentence.

H S E N O W S J S U D, Z Q' T

E R K V Z K W Z T J; H S E N O W S J

Q A S, Z Q' T W D T D K W H P

Answer

Start with ZQ'T it must be "it's". That leaves ERKVZKWZTJ ending with "is_". The last letter
must be "m" (as "t" or "h" is not possible after few try). It leaves 4-letter word OWSJ ending
with "m". Try some common words and "from" will fit. Similarly, try some trial-n-error for the
remaining words.

H S E N O W S J S U D, Z Q' T

c o p y f r o m o n e, i t' s

E R K V Z K W Z T J; H S E N O W S J

p l a f i a r i s m; c o p y f r o m

Q A S, Z Q' T W D T D K W H P

t w o, i t' s r e s e a r c h

Brain Teaser No : 00191

Decipher this sentence.

B R W Q H L F K W H J K Q I B W K

Q I C E D W Z B G W K K M I K E
 Z B G Q H S K Z B G J K Z K W

B U U Z B G J D B H F W.

Answer

Start with ZBG and ZBGJ. It should be either "the/then" or "you/your" combination as they
appear more.

B R W Q H L F K W H J K Q I B W K

o b s t a c l e s a r e t h o s e

Q I C E D W Z B G W K K M I K E

t h i n g s y o u s e e w h e n

Z B G Q H S K Z B G J K Z K W

y o u t a k e y o u r e y e s

B U U Z B G J D B H F W.

o f f y o u r g o a l s.

Brain Teaser No : 00348

There are 10 statements written on a piece of paper:

1. At least one of statements 9 and 10 is true.

2. This either is the first true or the first false statement.
3. There are three consecutive statements, which are false.
4. The difference between the numbers of the last true and the first true statement divides the
number, that is to be found.
5. The sum of the numbers of the true statements is the number, that is to be found.
6. This is not the last true statement.
7. The number of each true statement divides the number, that is to be found.
8. The number that is to be found is the percentage of true statements.
9. The number of divisors of the number, that is to be found, (apart from 1 and itself) is greater
than the sum of the numbers of the true statements.
10. There are no three consecutive true statements.

Find the minimal possible number?

Submitted by : Milind Gadagkar
Answer

The numebr is 420.

If statement 6 is false, it creates a paradox. Hence, Statement 6 must be true.

Consider Statement 2:

• If it is true, it must be the first true statement. Otherwise, it creates a paradox.

• If it is false, it must be the second false statement. Otherwise, it creates a paradox.

In both the cases, Statement 1 is false.

As Statement 1 is false, Statement 9 and Statement 10 both are false i.e. there are three
consecutive true statements.

1 2 3 4 5 6 7 8 9 10
False - - - - True - - False False

Let\'s assume that Statement 3 is false i.e. there are no three consecutive false statements. It
means that Statement 2 and Statement 8 must be true, else there will be three consecutive
false statements.

1 2 3 4 5 6 7 8 9 10
False True False - - True - True False False

Also, atleast two of Statements 4, 5 and 7 must be true as there are three consecutive true
statements.

According to Statement 8, the number that is to be found is the percentage of true statements.
Hence, number is either 50 or 60. Now if Statement 7 is true, then the number of each true
statement divides the number, that is to be found. But 7 and 8 do not divide either 50 or 60.
Hence, Statement 7 is false which means that Statement 4 and 5 are true. But Statement 5
contradicts the Statement 8. Hence, our assumption that Statement 3 is false is wrong and
Statement 3 is true i.e. there are 3 consecutive false statements which means that Statement
8 is false as there is no other possibilities of 3 consecutive false statements.

Also, Statement 7 is true as Statement 6 is not the last true statement.

1 2 3 4 5 6 7 8 9 10
False - True - - True True False False False

According to Statement 7, the number of each true statement divides the number, that is to be
found. And according to Statement 5, the sum of the numbers of the true statements is the
number, that is to be found. For all possible combinations Statement 5 is false.

There 3 consecutive true statements. Hence, Statement 2 and Statement 4 are true.
 1 2 3 4 5 6 7 8 9 10
False True True True False True True False False False

Now, the conditions for the number to be found are:

1. The numebr is divisible by 5 (Statement 4)

2. The numebr is divisible by 2, 3, 4, 6, 7 (Statement 7)
3. The number of divisors of the number, that is to be found, (apart from 1 and itself) is
not greater than the sum of the numbers of the true statements. (Statement 9)

The minimum possible number is 420.

The divisors of 420, apart from 1 and itself are 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35,
42, 60, 70, 84, 105, 140, 210. There are total of 22 divisors. Also, the sum of the numbers of
the true statements is 22 (2+3+4+6+7=22), which satisfies the third condition.