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]]>**American philosopher and logician George Boolos described the above riddle which was devised by Raymond Smullyan and published it in the Harvard Review of Philosophy in 1996. Boolos called it “The Hardest Logic Puzzle Ever”. You can read about making this puzzle even harder on the Physics arXiv Blog.**

S OME YEARS AGO, THE LOGICIAN AND PUZZLE-MASTER

Raymond Smullyan devised a logical puzzle that has no challengers I know

of for the title of Hardest Logical Puzzle Ever. 1’11 set out the puzzle here,

give the solution, and then brietly discuss one of its more interesting aspects.

The puzzle: Three gods A, R, and C are called, in some order, True, False, and

Random. True always speaks truly, False always speaks falsely, but whether Random

speaks truly or falsely is a completely random matter. Your task is to determine the

identities of A, R, and C by asking three yes-no questions; each question must be

put to exactly one god. The gods understand English, but will answer all questions

in their own language, in which the words for “yes” and “no” are “dam and “ja,” in

some order. You do not know which word means which2

Before I present the somewhat lengthy solution, let me give answers to certain

questions about the puzzle that occasionally arise:

- It could be that some god gets asked more than one question (and hence that

some god is not asked any question at all). - What the second question is, and to which

god it is put, may depend on the answer to the

first question. (And of course similarly for the - Wheather ranom speaks truly or not should

be thought of as depending on the flip of a

coin hidden in his brain: if the coin comes

down heads, he speaks truly; if tails, falsely. - Random will answer da or ja when asked any
The Solution: Before solving The

Hardest Logic Puzzle Ever, we will set out and

solve three related, but much easier, puzzles.

We shall then combine the ideas of their solutions

to solve the Hardest Puzzle. The last two

puzzles are of a type that may be quite familiar

to the reader, but the first one is not well

known (in fact the author made it up while

thinking about the Hardest Puzzle).

Puzzle 1: Noting their locations, I place two aces and a jack face down on a

table, in a row; you do not see which card is placed where. Your problem is to

point to one of the three cards and then ask me a single yes-no question, from the

answer to which you can, with certainty, identify one of the three cards as an ace. If

you have pointed to one of the aces, I will answer your question truthfully.

However, if you have pointed to the jack, I will answer your question yes or no,

completely at random.

Puzzle 2: Suppose that, somehow, you have learned that you are speaking not

to Random but to True or False – you don’t know which – and that whichever

god you’re talking to has condescended to answer you in English. For some reason,

you need to know whether Dushanbe is in Kirghizia or not. What one yes-no

question can you ask the god from the answer to which you can determine whether

or not Dushanbe is in Kirghizia?

Puzzle 3: You are now quite definitely talking to True, but he refuses to

answer you in English and will only say da or ja. What one yes-no question can you

ask True to determine whether or not Dushanbe is in Kirghizia?

**HERE’S ONE SOLUTION TO PUZZLE 1: POINT TO THE**

middle card and ask, “Is the left card an ace?” If I answer yes, choose

the left card; if I answer no, choose the right card. Whether the middle

card is an ace or not, you are certain to find an ace by choosing the left

card if you hear me say yes and choosing the right card if you hear no. The reason

is that if the middle card is an ace, my answer is truthful, and so the left card is an

ace if I say yes, and the right card is an ace if I say no. Rut if the middle card is the

Jack, then both of the other cards are aces, and so again the left card is an ace if I say

yes (so is the right card but that is now irrelevant), and the right card is an ace if I

say no (as is the left card, again irrelevantly).

To solve puzzles 2 and 3, we shall use iff

Logicians have introduced the usehl abbreviation “iff,” short for “if, and only

if.” The way “iff works in logic is this: when you insert “iff’ between two statements

that are either both true or both false, you get a statement that is true; but if

you insert it between one true and one false statment, you get a false statement.

Thus, for example, “The moon is made of Gorgonzola iff Rome is in Russia” is

true, because “The moon is made of Gorgonzola” and “Rome is in Russia” are

both false. But, “The moon is made of Gorgonzola iff Rome is in Italy” and “The

moon lacks air iff Rome is in Russia” are false. However, “The moon lacks air iff

Rome is in Italy” is true. (“Iff has nothing to do with causes, explanations, or laws

of nature.)

To solve puzzle 2, ask the god not the simple question, “Is Dushanbe in

Kirghizia?” but the more complex question, “Are you True iff Dushanbe is in

Kirghizia?” Then (in the absence of any geographical information) there are four

possibilities:

1) The god is True and D. is in K: then you get the answer yes.

2) The god is True and D. is not in K.: this time you get no.

3) The god is False and D. is in K.: you get the answer yes, because onlyone statement is true, so the correct answer is no, and the god, who is

False, falsely says yes.

4) The god is False and D. is not in K.: in this final case you get the

answer no, because both statements are false, the correct answer is yes, and

the god False falsely says no.

So you get a yes answer to that complex question if D. is in K. and a no answer if it

is not, no matter to which of True and False you are speaking. By noting the answer

to the complex question, you can find out whether D. is in K. or not.

The point to notice is that if you ask either True or False, “Are you True iff X?”

and receive your answer in English, then you get the answer yes if X is true and no

if X is false, regardless of which of the two you are speaking to.

The solution to puzzle 3 is quite similar: Ask True not, “Is Dushanbe in

Kirghizia?” but, “Does da mean yes iff D. is in K.?” There are again four possibilities:

1) Da means yes and D. is in K.: then True says da.

2) Da means yes and D. is not in K.: then True says ja (meaning no).

3) Da means no and D. is in K.: then True says da (meaning no).

4) Da means no and D. is not in K.: then both statements are false, the

statement “Da means yes iff D. is in K.” is true, the correct answer (in

English) to our question is yes, and therefore True says ja.

Thus you get the answer da if D. is in K. and the answer ja if not, regardless of

which of da and ja means yes and which means no.

The point this time is that if you ask True, “Does da mean yes iff Y?” then you

get the answer da if Y is true and you get the answer ja if Y is false, regardless of

which means which.

Combining the two points, we see that if you ask one of True and False (who

we again suppose only answer da and ja), the very complex question, “Does da

mean yes iff, you are True iff X?” then you willget the answer da ifX is true andget

the answer ja ifX is false, regardless of whether you are addressing the god True or

the god False, and regardless of the meanings of da and ja.

We can now solve The Hardest Logic Puzzle Ever.

Your first move is to find a god who you can be certain is not Random, and

hence is either True or False.

To do so, turn to A and ask Question 1: Does da mean yes i’ you are True zffB

is Random? If A is True or False and you get the answer da, then as we have seen,

B is Random, and therefore C is either True or False; but if A is True or False and

you get the answer ja, then B is not Random, therefore B is either True or False.

But what if A is Random?

If A is Random, then neither B nor C is Random!

So if A is Random and you get the answer da, C is not Random (neither is B,

but that’s irrelevant), and therefore C is either True or False, and if A is Random and you get the answer ja, B is not random (neither is C, irrelevantly), and therefore

B is either True or False.

Thus, no matter whether A is True, False, or Random, if you get the answer da

to Question 1, C is either True or False, and if you get the answer ja, B is either

True or False!

Now turn to whichever of B and C you have just discovered is either True or

False – let us suppose that it is B (if it is C, just interchange the names B and C in

what follows) – and ask Question 2: Does da mean yes iff Rome is in Italy? True

will answer da, and False will answer ja. Thus, with two questions, you have either

identified B as True or identified B as False.

For our third and last question, turn again to B, whom you have now either

identified as True or identified as False, and ask Question 3: Does da mean yes iffA

is Random?

Suppose B is True. Then if you get the answer da, then A is Random, and

therefore A is Random, B is True, C is False, and you are done; but if you get the

answer ja, then A is not Random, so A is False, B is true, C is Random, and you are

again done.

Suppose B is False. Then if you get the answer da, then since B speaks falsely,

A is not Random, and therefore A is True, B is False, C is Random, and you are

done; but if we get ja, then A is Random, and thus B is False, and C is True, and

you are again done. FINIS.

Well, I wasn’t speaking falsely or at random when I said that the puzzle was

hard, was I?

A brief remark about the significance of the Hardest Logic Puzzle Ever:

There is a law of logic called “the law of excluded middle,” according to which

either X is true or not-X is true, for any statement X at all. (“The law of non-contradiction”

asserts that statements X and not-X aren’t both true.)

Mathematicians

and philosophers have occasionally attacked the idea that excluded middle is a logically

valid law. We can’t hope to settle the debate here, but can observe that our

solution to puzzle 1 made essential use of excluded middle, exactly when we said

“Whether the middle card is an ace or not. …” It is clear from The Hardest Logic

Puzzle Ever, and even more plainly from puzzle 1, that our ability to reason about

alternative possibilities, even in everyday life, would be almost completely paralyzed

were we to be denied the use of the law of excluded middle.

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]]>and three apples do cost?

How can Ram be behind his wife, when she is behind him?

131. What would you do if you find a fire station burning?

132. What would you do if you find a fire station burning where there is no nearby fire

station?

133. On which side of the cat is the greater fur (hair) contained?

134. What is that you can hold it only with your right hand, but not with your left?

135. A man walked down a lonely country lane with no streetlights. There was no moon.

He was dressed all in black. Suddenly he heard a speeding car turned towards him from

the side lane. The car did not have its headlights on. There was no foot-path or room for

him to step out of the way and avoid being struck by the car. But yet, the driver of the car

screeched to a halt just in time in fraction of a second. How did the driver see?

136. I want to pluck a mango from the tree. A peacock is sitting just by the side of the fruit.

How can I get the same fruit without disturbing the bird?

137. I inserted seven doughnuts to a rope and tied the two ends of it. I wanted to eat a

doughnut without cutting the rope or breaking doughnut. How?

138. In a running race, if you overtake the person running second, where (which position)

would you be?

139. If you overtake the last… then where would you be?

140. A dog is tied to a 10 meters long rope. A bone is 15 meters away. The dog got the

bone. How?

141. Price of an article goes up by 10% and after one year comes down by 10%. When is

the price at a lower level? Before raise or after the fall or equal to original?

142. Are you adventure oriented? In a time machine you can go to future or past and

return to exactly the same spot in space, after one hour. Would you try if it comes free of

cost?

143. Here is an interesting question based on maths and physics. The TV news says that

the present day’s temperature in Kashmir is 0 degrees Celsius and it would be twice colder

the next day. What would be the temperature the next day?

144. If I show you a painting and say, ‘His father is my father’s son’, who is he to me, if I

have no brothers? Is it me or my son or my father or my grand father?

145. This question is to test your high quality logical perception. You are at a three-road

junction and confused which one leads to your destination Rampur. You find two brothers

standing there and you know that one is ‘always’ a liar and the other is always a truthteller.

But don’t know who is a liar and who is a truth-teller. Can you find your route by

asking just ‘only one’ of them ‘only one question’. How you can?

146. Here is a more complicated question. Three men are standing at a three road

junction. You’re not sure either to turn left or right to reach your destination. One of these

men tells always the truth, one always lies and the third tells either the truth or lie. Each of

the three men knows each other, but you don’t know who is who. If you can ask only one

of these men (chosen at random, since you don’t know which man is who) only one yes/no

question, what question would you ‘frame’ to determine the correct road?

147. Test your quick reflexes. While trekking through a remote jungle I was captured by

cannibals. The chief told me, “You may now speak your last words. If your statement is

true, we will burn to kill you in flames. If your statement is false, we will boil to kill you in

oil”. I thought for a moment, and made my statement. Perplexed, the clever cannibal chief

realised he could do nothing but let me go. What did I tell them?

148. The following problem was posed at an M. N. C interview. You are shown three

boxes with labels that contain respectively oranges, apples and a mixture of both of them.

You were told that all labels were wrongly pasted on the boxes. You are asked to close your

eyes and put your hand into any box of your choice and blindly take one fruit. You can now

open your eyes, see the fruit in your hands. You are asked to re-paste the labels correctly.

Can you? If so how?

149. This is a question on your capacity to shift your paradigm. A doctor and his (own) son

met with a car accident. The doctor’s hand was broken. The son is rushed to the hospital

with a brain injury. In the operation theatre, the surgeon sees the boy and says, “I can’t

operate on this boy, he is my own son!” How can this be?

150. When compared to the previous question, this is more complicated and tests your

capacity to think beyond normal limitations. A doctor, his wife and their own son were

going in a car and met with an accident. The doctor broke his hands, other had a head

injury, but the mother escaped. Outside the operation theatre, the mother was weeping,

and inside the neurosurgeon says, “I can’t operate. He is my own son!” How can this be?

**TRUTH HEAD-ACHES:**

151. In a bank robbery, A, B and C are suspected robbers. A says B is guilty, B says C is

guilty and C says A is guilty. Who is/are the real culprit(s) if all are telling lies?

152. In a bank robbery, A, B and C are the suspects. A says B is guilty. B says C is guilty. C

says B is guilty. If two people are telling the truth, who is/are guilty?

153. In a bank robbery, among A, B and C, one is a sure culprit. A says B is guilty. B says A

is guilty. C says A is guilty. If nobody is telling the truth who is/are guilty?

154. In a bank robbery, A, B and C are the suspects. A says he is not guilty. B says he is not

guilty. C says, “B is guilty”. Who is the real culprit, if only one among them is telling the

truth?

155. This is a question to challenge your lateral thinking. Suppose you are going in a deep

forest on a stormy night. It is totally dark and you have to travel further three hours to

reach the nearby town. You have only one seat in your car. You noticed 3 people underneath a

tree. One is a doctor, who took you in his vehicle to the hospital, gave his blood and saved

your life when you were a kid. The other is a 90-year-old lady suffering from asthma

requiring immediate hospitalization. The third one is your dream girl/boy to meet whom

you would bargain anything. This is the opportunity for which you are dreaming since

long. Whom do you take in your car? Around 87% prefer to take the old lady and are called

sentimentalists. Approximately 22% prefer to give lift to the doctor. They are realists. 1%

are the materialists who of-course prefers to go with their dream person. What do you do?

156. “What is today?” I asked. “If tomorrow is yesterday, today is Saturday” he replied.

What is today?

157. A flock of sheep was going down on a narrow highway. There was a huge hillock on

the left side, and a deep valley on the right. A torrent river was violently flowing down the

valley. As the Sheppard was steering his herd, a truck came from behind blowing the horn.

The young driver was in a rush to take his ailing mother to the hospital. He urged the

Sheppard to move the sheep aside, so that he could pass through. The Sheppard declined

to do so, fearing that the crammed sheep dreaded by the horrifying sound of the truck,

might panic and fall down into the overflowing waters. The boy explained the situation.

But there was no other way except to follow the sheep slowly from behind till the road

widens, which would take another half an hour. The condition of the ailing mother was

deteriorating. Sensing the severity of the situation, the Sheppard was struck by an idea.

What was the idea?

158. A king wanted more warriors in his country. He proposed to increase the

population of male compared to female. Hitherto it was 1:1. He set down a law that

required every couple to continue having male children until they had their first female

baby and then to stop having children further. Excellent idea. First: Male baby? Continue

for another. Second male? Congratulations. Third female? Stop. The family has now two

males and one female. If your first baby is female, you cannot take risk of another baby, as

there is a possibility for the second one also being a female. The idea of the king appears to

be logical. After two generations what would have happened? How much would have been

the growth of males compared to females? Double? Triple?

159. Three soldiers have to cross a river. There is a boat and two children who can row it

and are willing to take the soldiers with them to the other side. But the problem is that the

boat can bear the weight of two children or only one soldier. Along with the soldier, even if

one child steps on, it would sink. One of the soldiers is intelligent and with his idea, all the

three went to the other side of the river and safely handed over the boat to the children.

What is the idea?

160. During an examination, a medico was asked to identify a femur that he recognised as

a human thigh bone. “How many of them do you have?” was the next question. The

student replied, “Two”. The examiner passed him and failed another student, who said

“Three”. He also failed two female students who said “four” and “Five” respectively. All the

three students appealed to higher ups and won the case after explaining their reasons.

What may be their reasons?

161. I wrote this story when I was 18 years old. This was my first story and was published

in a children magazine ‘Chandamama’. Solve this riddle: Unable to find any food or

charity, a beggar prayed God, “O God! Give me something. I promise to offer you half of

what I get today.” Amazingly he found a purse containing two hundred rupees. He was in

high spirits and spent everything. From next day his inner conscious started warning him

about God’s punishment. Day by day his agony and fear increased. Then one night he had

an idea and implemented it. Without paying a single pie to the God, he relieved from his

tension. What might have been the idea?

162. A lady listened to the continuous ringing of phone bell while reading a newspaper,

but does not bother to rise from the chair. Tell at least five reasons. The reasons may be

humorous or even stupid also, but this riddle is to test your caliber as to how fast can you

think of various probabilities.

163. I married an ugly, poor and unhealthy person. Pleased by my act, an angel offered

only one of the three to my spouse: Beauty, Money or Health. What should I take?

164. Happy with my answer for the above question, after giving health the angel wants to

make my spouse beautiful, but only for 8 hours a day. Which time should I prefer?

Morning? Afternoon? Evening? Night?

165. Why did a perfectly healthy office-going girl put a full plaster cast on her arm when it

was not injured in any way? Give at least four reasons.

166. A person wanted to purchase a talking bird, went to an auction and expected the

price to be thousand rupees. But the bid went up to ten thousand. There were no other

competitors. Still, the bid rose to such a huge amount. What would have happened?

167. A person demonstrates a fake note manufacturing machine. He inserts a white paper

into a printing machine and a perfect thousand rupee note comes out from the other side.

The buyer also personally inserts a paper and gets another note. Both the notes are

scrutinized by Reserve Bank officials and certified them as the original. The buyer purchases

the machine for one million rupees and later finds out that he has been cheated. How?

168. Fill the stars with numbers from 1 to 12, using every number only once. The total of 4

stars connected by lines should be 26.

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]]>one, which weighs less than others. You are given a balance machine but no weighing

measures. You can use the balance machine three times only. The balance machine tells

you just which side weighs more. How can you find the odd coin just by weighing the

available coins?

52.Go through the previous question about gold coins. Because one of it is of less weight,

you may have solved it easily. But if one of it is of different weight (you don’t know

whether the odd coin is of more weight or less weight) then the question becomes more

complicated. Think whether you can solve it. If not, see the answer. If you are confused

with the answer also, then go to the next question and try to understand it and answer.

Revert back to this question again, to understand the technique. Don’t leave it frustrated.

53.A king wanted to present one gold toy of ten grams each, to every child in his kingdom.

He employed 100 artisans. Per day each artisan produced ten toys and hands them over to

the treasurer. After a month, the king knew that one of the artisans is cheating by

swindling 1 gram of gold per toy. Next day he went to the treasury in the evening when the

100 artisans brought their manufactured toys. The king has a weighing machine and

measuring stones. Using the machine only once, he was able to find the culprit. How?

13

54. Here is a riddle to test your reasoning skill. This can be done with a computer or

without it. Even a computer may take few minutes to answer. They say Ramanujam, the

mathematic wizard could calculate the answer in 10 minutes in computer-way. As told

earlier, there is another way of doing it. He could do it in few seconds in such a more

sensible way. Don’t rush for the answer. Think. Use your commonsense. A young girl was

walking towards a Shakti temple at 3 km per hour. Ram crossed her on a motorcycle at a

speed that is 20 times more than her. He wanted to give lift to her but could not dare. He

travelled for 3 minutes and on seeing temple of Shakti, he got courage and returned. He

saw her but was not courageous still. He returned back towards the temple, reached it and

again got inspired and returned. The process continued. In the final trip, he stood near the

temple and prayed Goddess Shakti “Please give me courage”. The girl, having reached the

temple, said from behind, “Shakthi the power… is not there in that stone. It is in you.

Discover it.” Now the question is: How much distance did Ram travel in total?

55. A had 5 chapattis, B had 3 and C had nil. They all ate equally and C paid 8/- to them as

the price for what he had eaten. How much A and B should get from the said amount?

Choose from the 4 answers: A5, B3 / A7, B1 / A4, B4 / none of these three.

56.Suppose a=b. With this equation, I will prove that a + b = b in four steps. Find out

where (in which step) I went wrong?

Step one: if a=b, then a²=ab.

Step two: Deduct b² from both: (a² – b²) = (ab – b²).

Step three: (a + b) (a – b) = b (a – b).

Step four: Deduct (a-b) from both: a + b= b. How is this possible? In which step lies the

mistake?

57. Here is an excellent puzzle to test your reasoning skills. The five pandavas: Dharma

Raja, Bheema, Arjuna, Nakula and Sahadeva were sleeping in the Red-wax house and their

enemies burnt it. The pandavas were to escape through a tunnel. Only two people could go

through the tunnel at one time. Moreover, it was totally dark and without a torch they

could not proceed. They had only one torch. It means, two people should go out, and then

one had to take the lamp inside and accompany another one out. Total 4 trips. It would

take for Nakula and Sahadeva 5 minutes and Arjuna 10 minutes to come out. Bheema

would take 20 and Dharma 25 minutes respectively to come through the tunnel, as one

was hefty and another was old. This is an arithmetical problem and has no twists. How

much minimum time it would take?

58.In the above question, suppose they knew that the cave was going to collapse exactly in

60 minutes and they had to escape within the said time. If Nakula takes the responsibility

of bringing all the other four, it would take 75 minutes (if this is what you worked out in

previous question). But if you are more intelligent, there is a way to make it in 60 minutes.

How?

59.If you are asked to find out the value of A (other than zero), when A+A= A x A, you

would answer that A = 2, as 2 + 2 = 2 x 2. Taking this as an example, find out the different

values of a, b, c, if a + b + c = a x b x c.

60.“Intellectual endurance” is the staying power, the capacity to persist without getting

distracted. At one point your brain ceases to cooperate, but please don’t stop doing this

calculation. Take a few minutes rest and start again. This is one way of developing

intellectual endurance. Take a ‘single digit number’ and a ‘three digit number’ of your

choice… For example, suppose the numbers are: 8 and 156, write down on a paper as 8-

156. Go on adding 13 to the first number and deduct 7 from the later. Do it simultaneously

(Here is the example. your first number is 8 – 156. Hence your second number would be

21-149, third 34-142). At the end… what are your final figures when you reach the single

digit answer on the right hand side? Don’t jump to calculate end figures, do it step by step

to test your patience.

14

61. From the following diagram choose the correct answer: 1) AB is lengthier than CD.

2) AB is shorter than CD. 3) AB is equal to CD.

62. A milkmaid adds 4 litres of water to 2 litres of milk before distribution. By mistake she

added 2 titres water to 4 litres of milk. How much more water has she to add to rectify her

mistake?

63.A painter should mix 6 litres of paint, consisting of 4 litres of white and 2 litres of

black. But by mistake he mixed 2 litres of white and 4 litres of black. How much minimum

did he have to pour out to correct his mistake before adding the extra white paint?

64.What is “Two plus two by two?”

65.What is a plus b minus a plus b?

FOOD AND TRAVEL: These questions are to test your hyperactivity. Answer fast.

66.If 1 hen lays 1 egg in 1 day, how many eggs 2 hens lay in 2 days?

67. The question is an arithmetical question, not based on logic. If 4 hens lay 4 eggs in 4

days, how many eggs 2 hens lay in 2 days?

68.This is a logical question. How many eggs can a boy eat with empty stomach?

69.There are six eggs in the basket. Six people take each one of the eggs. One egg is left in

the basket. How could this be possible?

70.If two hens lay 2 eggs in 2 days, how many eggs does one hen lay in 1 day?

Arithmetically the answer would be “half-egg” which is not logical. Think of various

alternatives and give at least three logical probable answers for ‘one egg’.

71. A cook in a restaurant has a four minute hourglass, and a seven minute hourglass,

made of sand that shows the exact time. A customer orders a nine-minute egg. Using the

two glasses, how to cook exactly in the time given, not to a difference of even few seconds?

72.I take a private car from my house to my office located at the outskirts of the city in the

morning and back home in the evening. It costs me 300 rupees everyday. One day the taxi

driver informed me that there are two students who wish to go to their college every day in

the morning along with me! Their get-in point is exactly halfway between my house and

office. Their college is adjacent to my office. On the first day I told them, “If you tell me the

mathematically correct price that each one of you should pay for your portion of the trip, I

15

will let you travel free along with me.” How much should the individual student pay for

his journey?

73. A passenger train starts at 5 p.m. from Agra and reaches Delhi at 10 p.m. From Delhi, a

train starts for every one hour throughout the day, at 5.30, 6.30 7.30 etc. How many such

trains would cross the passenger rail before it reaches Delhi?

74. The distance from Station to Bus-stand, Via Tank Bund is 8 miles. From Tank Bund to

Bus-stand via Station is 7 miles. From Station to Tank Bund via Bus-stand is 11 miles.

Calculate the distances between: 1. Station and Bus-stand, 2. Station and Tank Bund and

3. Bus-stand and Tank Bund.

75. There are some eggs in each bucket, named A, B, C, D, E. If A = 5; B+A =6; E+B =C;

E+C+B = 8, choose the values of A, B, C, D, E from 1, 2,3,4,5.

76.As in the same question above, find out the values of A, B, C, D, E from 1, 2,3,4,5 if D+B

= A+C; 2E =C+5; D+C = E. This is a more complicated question.

77. Three friends divide eggs from a bag equally. After each of them eat 4 eggs, the total

number of eggs remaining with them, is equal to 1/3 of total eggs. Find the original

number of total eggs.

78.You have two cups, one containing orange juice and one containing equal amount of

lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a

teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in

the orange juice or more orange juice in the lemonade?

79.A student is studying for his examinations and the lights go off. It is around 1:00 AM.

He lights two uniform candles of equal length but one is thicker than the other. The thick

candle is supposed to last 6 hours and the thinner one illuminates for 4 hours. When he

finally goes to sleep, the length of the thick candle is twice longer than the thin one. For

how long does the student study in candle light?

80.There are 3 switches, 1, 2 and 3 in a hall in the ground floor. One of them is connected

to a dining room bulb in the third floor. You can’t see it from the ground floor, whether the

dining room light is on or off. How can you identify the correct switch? You can on and off

the switches as many times as you want, but you are supposed to go to the second floor

dining room only once and should announce the switch number from there.

81. A man decides to buy a horse for 600 rupees. After a year, he sells it for 700. He buys it

again for 800. And finally sells it for 900. What is his overall profit?

82.A swimmer jumps from a bridge into a canal and swims 1 kilometre against the stream.

There he passes a “floating cork” coming in opposite direction, going towards the bridge.

He continues swimming forward for half an hour more and then turns around and swims

back to the bridge. The swimmer and the cork arrive at the bridge at the same time. How

fast does the water in the canal flow?

83.Two cars (A and B) are travelling in opposite direction with 60 and 40 miles per hour.

The distance between them is 100 miles. A bird starts along with car A, and flies at a speed

of 80 miles per hour towards B. When it reaches car B, it turns back and when it reaches

the car A, again it turns to the opposite direction. What is the total distance that the bird

has travelled when the two cars met?

84.You drive at 20 mph from point A to B and return at 30 mph. what is the average

speed?

85.If you drive at 20 mph from point A to B, how fast must you drive back to attain an

average speed of 40 mph?

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]]>=> I wanted to gamble in a match between India and England. The odds were 2:1 i.e., if I

bet 100 on India, I get 200 more. If I bet 100 on England I get 100 more. If I invest RS. 50

each in both the countries and if India wins I gain 100 rupees on India and lose 50 on

England. Hence my total profit would be RS. 50/- (+100-50). But if England wins, there

would be neither profit nor loss (-50+50). What would be the safest bet to get the

maximum profit? How much I should bet on India and England so that I get maximum

amount, irrespective of which country wins.

=> At a cricket betting, a fortune-teller at the gate said, “For ten rupees I will tell you the

scores. You can bet on that. If it goes wrong, I would give you 1000/- as compensation”.

Should I take the offer?

=> Think before answering. It is not as simple as it appears to be. Don’t rush to turn the

pages to find out the answer at the end. Take time and think: In a fifty over one-day

the international match, 49.4 balls are bowled. Last two balls… Seven runs to win… it is ninth

wicket partnership… Last two batsmen are at 94 runs each. The team won and both

batsmen made centuries. How could it be possible? Don’t think of a no-ball, free hit wide,

hitting the helmet etc because… on no-ball if the batsman hits a six it adds 7 (seven) runs

to the team score and it wins. Then how the runner also gets 100 runs? This puzzle is more

complicated than what you think. Try.

=> In an annual state tournament 5 cricket teams participate. The champion team is

chosen for this tournament by the usual elimination scheme. That is, the 5 teams are

divided into pairs, and the two teams of each pair played against each other. The loser of

each pair is eliminated, and the remaining teams are paired up again, etc. How many

games must be played to determine a champion?

=> In the above competition, if the participating teams are 50, then how many games are

to be played?

=> Three men go to a Lodge where they were told that the room rent is 30. They shared 10

each. Later the receptionist realized that the rent is 25 only. He sent back 5 rupees through

the boy. They paid him 2/- as a tip and kept one rupee each. In other words, each has parted

with rupees 9 towards rent, the total amounting to 27. The boy was paid 2 rupees. Total: 29.

Where has the remaining one rupee gone?

=> A 16 meters cable is attached to two 15 meters high pillars. At its lowest point, the cable

hangs 7 meters above the ground. What is the distance between two pillars?

=> Which of these numbers can be equally divided by 2? 5, 6, 7, 8.

=> This is an interesting question believed to be prepared by Mathematics wizard

Sakuntala Devi. If a clock takes two seconds to strike two bells, how much time does it take

to strike three bells?

=> If a clock takes 5 seconds to strike 5 pm, how long will it take to strike 10 pm?

50.The time between first and last ticks is 30 seconds at 6 pm. How long does it tick at 12

o’ clock?

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]]>The post Intelligence, fun and amusement appeared first on Readmyhelp.

]]>two-and-half feet?” I asked a boy, who replied, “Two-and-half legs”. He is an

institution that taught him rapid mathematics five hours a day. He is really good in

multiplications and is able to multiply a four digit number with another three-digit

the number within a minute. Without understanding what the boy is lacking, the proud

parents claim that he is brilliant in maths.

Instead of blaming the child for securing low ranks, parents should try to trace out his

phobias and fields of deficiency. The concept of ‘education with entertainment’ includes

identifying the limitations of a child through fun, cheerfulness, and amusement.

6

“Our child is intelligent and used to get good marks earlier. But we don’t know what’s

happening now” many parents complain. A child cannot be said to be intelligent, just

because he scores good ranks. Up to school level, students can get good ranks, if they are

simply industrious.

‘Wisdom’ includes both memory and intelligence. When a student solves a mathematical

equation faster than others, it is his intelligence. When a student is good in history he is

said to be industrious.

Whenever you are bored or feel sleepy, engage in mathematics. “Mathematics is the poetry

of logical ideas,” said Newton. Developing interest in mathematics is one of the best virtues

in the elementary stage of education. Studying math is different from studying other

subjects, as ‘study’ is of two types, Active and Passive. Mathematics requires active study.

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]]>The post Tips to master in maths appeared first on Readmyhelp.

]]>on your intelligence. It is one of the few subjects, wherein you can score hundred percent

marks to enhance your overall percentage.

Many students fear maths. But it’s an easy and interesting subject, once you understand

the basics. Be thorough in them. Without comprehensive knowledge about fundamental

formulas, techniques, multiplication tables, laws, and theorems you cannot expect to be

good at maths.

Unlike other subjects, each lesson in maths is built on the previous ones. Falling a day

behind puts you in a confused position. Never hesitate to ask questions. A little-uncleared

doubt now leads to a huge roadblock in future.

There are two steps in mastering maths. It is by Practice (taking interest in solving

various types of problems) and Application (solving a particular problem in different

ways). Understand the problem first. Devise a plan. Apply your skills and techniques.

While working on the equation, draw the nearest and correct route to the answer. If you

fail to reach the target, use other variables. This applies to management accounts,

statistics, costing… and life also.

“If some people believe that mathematics is tough, it is only because they do not realize

how complicated life is,” said Ramanujam, the maths pundit. ‘Reasoning’ is the backbone

for maths. Failure in ‘not getting the correct solution’ teaches you how to look back to

locate your mistake, amend your equations and arrive at a correct solution. This applies to

real life also.

Convert your life problem into simple mathematics. Draw a formula. Locate the nucleus of

the crisis. Once you are clear about the cause of your problem, automatically you would

know the method of approach to sorting it out.

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