1. A man woke up one morning to find that one of the wheels of his car had a completely flat tire. Despite this he set off in his car and drove 100 miles to visit a customer. He then drove 100 miles home. He did not repair or inflate the flat tire. How did he manage to make the journey?

The flat tire was on the man's spare wheel which he kept in the car trunk. The four wheels he drove on all had properly inflated tires.

2. A man threw something away. He then paid someone else twenty dollars to try to find it but the search was unsuccessful. Later the man found it easily himself. How?

The man fell overboard from a small boat at the seashore. He could not swim well and got into difficulties so he threw away the expensive and heavy binoculars around his neck. He was rescued. He then offered a swimmer a reward to dive down and recover his binoculars. This effort was unsuccessful. Later, however, when the tide went out he was able to pick them up off the sand.

3. A man was changing a wheel on his car when the four nuts used to hold the wheel in place well into a sewer drain and were lost. He was afraid he ws stuck there, but a passing boy made a very useful suggestion which enabled the man to drive off. What was the boy's idea?

The boy suggested that the man take one wheel nut off each of the oyher three wheels in order to attach fourth wheel. Once he had done this, the man could safely drive to the nearest garage with each wheel firmly attached by three nuts.

4. A manhole is a hole which allows someone to gain access to the sewers or other pipes which are below ground. Our local town council recently decided that all the town's manhole covers should be changed from square to round ones. We are user to the town council making silly decisions, but this time they were absolutely right. why?

A square or rectangular manhole cover can fall down the hole, while a round manhole cover cannot. The square cover will fit down the diagonal of the hole(unless the rim it sits on is very large) but no matter how you turn a circle it never measures less than its diameter. So for safety and practicality all manhole covers should be round.

5. A man lies dead in a field. Next to him is a long piece of cord. How did he die?

Incredible as it may seem, some people enjoy leaping off high buildings or bridges with a length of elastic cord fastened to them. This pastime is known as bungee jumping. The poor man in this situation died when he jumped from a high cane in the field and his bungee cord broke.

6. The famous penny black, the world's first postage stamp, was introduced in England in 1840. The idea of postage stamps was a great success and was taken up worldwide. Yet the penny Black was in use for only one year before it was replaced by the Penny Red. Why?

The postmark used at that time was always black. It was therefore difficult to tell whether a stamp had been frankled or not. This led to people reusing used stamps. On a Penny red the black postmark was clearly visible.

7. A man had a book which was worth $40,000. Why did he deliberately destroy it?

The man actually owned two copies of the valuable book. By destroying one copy he increased the value of the other.

8. A man parked his car outside a bank and rushed in. He held up twenty-five people and ran out with $200. A policeman who saw the whole incident stopped the man. He told him off and then let him go. Why?

When the man parked his car outside the bank he held up twenty-five people who were stuck in traffic behind him. The policeman told him not to park like that again.

9. How do the publishers of dictionaries or atlases protect themselves from pirates who would copy their work?

Publishers normally include a nonexistent word or a non-existent island in a dictionary or atlas, respectively. If it then appears in somebody else's work, they have clear evidence of copying.

10. Ornithologists now agree that there is a very good reason why birds' eggs are generally narrower at one end than the other. What is the reason?

A spherical or oval egg would roll in a straight line. How-ever, an asymmetrical egg, which is narrower at one end than the other, will tend to roll in a circle. (Try it with a normal hen's egg.) if the eggs are on a cliff edge or other precarious place, the tendency to roll around rather than straight is a distinct advantage.

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11. A man went out for a drive. A day later he was found dead in the car. The car had not crashed. How had he died?

The man drove his car to the beach to watch the sunset over the waves. He fell asleep. The tide came in and seeped in around the car doors and windows. He awoke, but with the pressure of the water, he couldn't get out of the car. The water filled the car and drowned him. Later the tide went out and he was found dead in an empty car.

12. Visitors to a scenic mountain village were often amused by the village idiot. When offered a choice between a shiny 50-cent piece and a crumpled $5 bill, he would always happily choose the half-dollar. The bill was worth ten times as much, so why did he never choose it?

The so-called village idiot was smart enough to realize that as long as he kept choosing the 50-cent piece, people would keep offering him the choice. If he once took the $5 bill, the stream of coins would stop rolling in.

13. We all know that there is a way to get a ship into a bottle. How would you get a full-sized pear into a bottle without damaging the peer or breaking or cutting the bottle?

The fruit is grown in the bottle. The bottle is tied onto the branch shortly after the fruit starts to form.

14. We all know that there's a way to get a ship into a bottle. How would you get a full-sized pear into a bottle without damaging the peer or breaking or cutting the bottle?

The fruit is grown in the bottle. The bottle is tied onto the branch shortly after the fruit starts to form.

15. A man was found shot dead in his study. He was slumped over his desk and a gun was in his hand. There was a cassette recorder on his desk. When the police entered the room and pressed the play button on the tape recorder they heard, "I can't go on. I have nothing to live for." Then there was the sound of a gunshot. How did the detective immediately know that the man had been murdered?

The cassette had started at the beginning of the man's utterance. Who could have rewound it?

16. A man's lifelong ambition was to achieve a certain goal yet he insured himself against achieving it. What was the goal?

This is the true story from Japan. The man easd a keen golfer and his lifelong ambition was to score a hole in one. But this would prove very expensive as the custom at his golf club was that anyone who scored a hole in one had to buy all the other members a drink.

17. A child was born with its legs so wasted that it would never be able to walk. When they learned this, the child's parents were especially happy that the child was crippled rather than normal and healthy. Why?

This is a true story from India. The child was born into a family of beggars in Calcutta. The parents knew that a crippled child would earn more as a beggar than a healthy child would.

18. A French glove manufacturer received an order for 5,000 pairs of expensive sealskin gloves from New York department store. HE then learned that there was a very expensive tax on the import of sealskin gloves into the United States. How did he (legitimately) get the gloves into the country without paying the import tax?

The manufacturer sent 5,000 right-hand gloves to Miami and 5,000 left-hand gloves to New York. He refused to pay the duty on them so both sets of gloves were impounded. Since no body claimed them, both lots were subsequently sold off at auction. They went for a very low price (who wants 5,000 left hand gloves?). Naturally, it was the clever Frenchman who one with a very low bid at each auction.

19. A man stabbed his wife to death. He was alone with his victim before and after the crime. To throw the police off the scent he suddenly decided to leave false fingerprints one the murder weapon. How did he do it?

The man put his wife's big-toe print on the knife and left it beside the body. He could have used his own toe-print but that could have been later traced to him. Once his wife was buried, the "fingerprints" could never be traced.

20. A man was walking in country unfamiliar to him. He came to a crossroads where he found that the signpost showing the directions of the roads had fallen over. How did he find out which way to go?

The man knew the name of the town he had left that morning. So he replaced the sign so that it correctly named the direction he had come from. It would then be correct for all the other directions.

21. St. James Hospital handled all the accident cases for the city. They were kept especially busy by the large number of drivers and passengers injured on the city's roads. To improve the road safety, a law was passed making the wearing of seat belts mandatory. Drivers and passengers now started to wear seat belts in their cars. The frequency road accidents remained exactly the same. However, the hospital was now even busier handling road-accident victims than before. Why?

The wearing of seat belts was successful in reducing the number of deaths from road accidents. People who with-out seat belts would have been killed (and taken to the morgue) now survived but with injuries. Consequently more people were treated for injuries than before.

22. A man lies dead in a room, with a cord tied tightly around his neck. The door has been locked from the inside. Outside of the body, there is nothing else in the room. Remembering that one cannot choke oneself (one would pass out before dying.) how did you die

The cord around the man's neck was a piece of rawhide which he had soaked in water before entering the room. Once he had it tightly around his neck it naturally grew tighter as it dried.

23. A man was doing his job but was killed because he lacked a certain piece of furniture. Why

The man was a circus lion tamer who had unfortunately forgotten his chair when he had to face a bad-tempered lion!

24. A man challenged the Olympic 100-metres sprint champion to race over a short distance on the condition that he is allowed to choose the course. How does he manage to beat the champion? (N.B The solution to the preceding problem won't help you here.)

He challenged the Olympic champion to run up a ladder. Since he was the fastest window cleaner in Ireland he won easily!

25. A man challenged the Masters Golf champion to a round of golf on the condition that he be allowed to chose the time and place of their contest. The champion accepted the challenge but was easily defeated by the challenger. Why?

The challenger was a blind golfer and he arranged to play the champion at midnight on a dark night. The blind man was at no disadvantage in the dark but the champion could not see his ball to hit it. (Blind golfers do play matches and tournaments; they rely on others to indicate where their ball and the hole are.)

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26. Can you resolve this argument which arose at a recent bridge match? Spades were trumps. Which is more likely that a pair of players will have no spades dealt to them?

It is equally likely that one couple will have all the trumps as that they will have no trumps between them. For if they have all the trumps if must mean that the other pair has none and vice versa.

27. A visiting school superintendent noticed that whenever he asked one class a question all the children would put up their hands. Moreover, although the teacher always chose a different child to answer, the answer was always correct. Why?

The teacher instructed her pupils always to raise their hands when a question was asked whether they knew the answer or not. If they did not know the answer they should raise their left hand. If they were sure they know the answer they should raise their right hand. The teacher chose a different child each time, but always one who had raised his or her right hand.

28. Protagoras was a lawyer in ancient Greece. As an act of kindness he took on a poor but promising young man as a pupil. He agreed to teach him law but make no charge until the student had won his first case, when the student would repay the tuition fees. The young man gladly agreed to this plan. The student completed his training, and then decided that he did not want to practice law. Instead, he retired to the countryside to keep goats. Protagoras was disgusted at this waste of talent and training and dismayed that he would not be reimbursed for the tuition. He decided to sue his pupil in order to recover his fees. If the two men met in court to argue the case, who do you think would have won?

This is a paradox with no clear-cut answer. Both parties have a good case. It would be interesting to see it argued out in court. Whoever lost could claim to have won-the student in losing would still not have won a case, Protagoras in losing would ensure a first victory for his pupil. Some believe that the most likely outcome of such a situation, if it had come to trial, would have been victory for the student. He was after all under no obligation to practice law and up until that point he had not breached ever, he could sue a second time on grounds that the student had now won a case and was in breach of contract. Protagoras would therefore win the second case and recover his fees. Overall, Protagoras would have won. The student would be smart to choose not to represent himself but to select a good lawyer who could win the first case for him. In that case, since a pupil would still not have won a case, he would have won the contest.

29. At a fancy, upper-class dinner party a precious gold coin was being passed around the table for inspection when suddenly the lights went out. When the lights came on again the coin was missing. A search of each guest was ordered. One man refused to be searched. The police were under a saucer. Why did the guest refuse to be searched?

The man who refused to be searched was an aristocrat who had fallen on very hard times but was trying to keep up appearances. He was so poor, however, that he could scarcely afford to eat. So, while at the dinner, he secretly lined his pockets with food from the table to keep him going for the next few days. Obviously if he was searched his secret would be revealed and he would be humiliated.

30. A girl was eight years old on her first birthday. How could that be?

She was born on February 29, 1986. The year 1900 was not a leapt year (only centuries divisible by 400 are leap years), so the next February 29 fell in 1904 when she was eight. She was twelve on her second birthday.

31. A man suspected his wife of having an affair. One day he told her that he had been suddenly called away on business and would be out of town for a few days. He then left the house but returned an hour later. His wife was not there but he quickly discovered the name and address of her lover. How?

He reasoned that she would have called her lover so he simply pressed the redial button on their telephone. When the man answered with his name the husband told him that he had won a prize draw and asked for the address to which it should be sent.

32. At a children's hospital the patients loved to play with the cuddly teddy bears they had there. Unfortunately, the children liked them so much that the bears were disappearing at an alarming rate as the young patients took them home. How did the hospital solve this problem?

The hospital dressed all their teddy bears with bandages. Then they explained to the little children that the poor teddies had to say at the hospital for their own health and recovery. The children reluctantly but sympathetically agreed.

33. Although there are very few golf tour professionals who are left-handed, most clubs prefer to have left-handed golf pros as instructors. Why?

One of the most important tasks for the golf club professional is giving lessons. Most players are right handed. They can stand opposite a left-handed teacher and watch and copy him more easily. It is just like looking in a mirror, so it makes learning the correct style of swing easier.

34. As part of a school experiment girl was sent to the middle of a nearby city with instructions to collect a sample so that pollution levels could be measured. She was given a glass container with a removable but tight-fitting lid. Of course she noticed that the jar contained comparatively clean air from the school environment. How did she ensure that she excluded this air and retrieved an absolutely accurate sample of the city air?

The girl filled the jar with water at the school. When she reached the appropriate point at the city center she poured all the water out. What replaced it was a true sample of the surrounding air.

35. One day, in a crowded room, a supporter of the Brazilian soccer team saw a supporter of his team's great rivals, Argentina . The Brazilian fan walked over to the Argentinian fan and struck him a fierce blow. The Argentinian fan who had been knocked flat got up from the floor, turned around, and then thanked the man who had hit him. why?

The two men were in a restuarant. The Argentinian fan had a fishbone stuck in his throat and was chocking. The other man was quick-witted enough to give him a strong blow on the back, thereby dislodging the bone and saving his life .

36. Greenland is a huge country covered with snow and ice. Why did the man who discovered it call it Greenland?

In about 982 a Norseman, Eric the red, discovered Greenland. He wanted to encourage people to settle there so he called it Greenland to make it sound attractive. It is a very early example of deliberately misleading labelling.

37. At the end of the long hard boxing match one boxer was knocked out by the other. The judges agreed it was a completely proper victory. Yet during the course of the match no man threw a punch. What happened?

No man threw a punch because the boxing match was between two women boxers.

38. A man filled an empty barrel. It was then lighter than when he started. What did he fill it with?

The man filled the barrel with with holes! Since there was now less barrel it weighed less.

39. A young girl was listening to the radio. Suddenly it went off for a minute and thencame back on again. There was nothing wrong with the radio or with the program transmission from the radio mission from the radio station. She did not touch the radio controls. Why did it go off and on?

The girl was listening to the radio in her father's car. He drove through a tunnel and reception was temporarily interrupted.

40. Ben was 20 years old in 1980 but only 15 years old in 1985. How come?

Ben was born in the year 2000 B.C. So in 1985 B.C. he was 15 and in 1980 B.C. he was 20.

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41. Two sentries were on duty outside a barracks. One faced up the road to watch for anyone approaching from the north. The other looked down the road to see if anyone approached from the south. Suddenly one of them said to the other, "Why are you smiling?" How did he know that his companion was smiling?

Although the guards were looking in opposite directions, they were not back to back. They were facing each other.

42. A deaf man needed to buy a saw to cut some wood. He went into a hardware store. How did he indicate to the storekeeper that he wanted to buy a saw?

The deaf man says to the storekeeper, " I would like to buy a saw, please.

43. Two brothers were talking. One said, " I am fed up with living in Birmingham because I have to drive all the time. Why don't we move to london?" His brother replied, "But that would mean that I would have to drive all the time. " Why was this true?

The brothers were siamese twins, joined at the side. They lived in Birmingham, Albama. Because they drove on the right hand side of the road the steering wheel was on the left hand side of the car. The brother who sat on the left always drove. When they were in London, England, the other drove because the steering wheel was on the right hand side of the car.

44. A man got up at 9 a.m. He became so engrossed in his newspaper he did not have time to go out and shop as he had planned. At 11 a.m. he went for a flying lesson. He carefully followed all the instructions given to him by his instructor until he came in to land. He then ignored his instructor and crashed the plane killing them both. The accident would not have happened if he had gone shopping, which just goes to show how important shopping can be. Why should this be so?

The man had neglected to buy a new battery for his hearing aid. The old battery failed just as he was coming in to land and he therefore did not hear his tutor's crucial instructions.

45. 6) A man who was not wearing a parachute jumped out of a plane. He landed on hard ground yet he was unhurt. Why?

The plane was parked on the runway.

46. William's father was older than his grandfather. How did that happen?

Let's say that William's father was 60, his mother was 25, and his mother's father was 45. Because everyone has two grandfathers, it is quite possible for a maternal grandfather to be younger than one's father.

47. A man walked all the way from Dublin to Cork along main roads without passing a single pub. How did he manage that? (Pubs or " public houses," that is, bars, are very common in Ireland. )

The man did not pass a single pub because he went into every one!

48. Two men were playing tennis. They played five sets and each man won three sets. How did they do this?

The two men were partners playing doubles.

49. The 22nd and 24th presidents of the united states had the same mother and the same father, but were not brothers. How could this be so?

They were the same man. Grover Cleveland (1837 - 1908) served two terms as president of the United States, but the terms were not consecutive. He was president from 1885 to 1889 and from 1893 to 1897.

50. There where six apples in a basket and six girls in the room. Each girl took one apple, yet one apple remained in the basket how?

The first five girls each took an apple. The sixth girl took the basket as well as the apple in it.

51. What are the next three numbers in the given series?

1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 ?

The next three numbers in the series are 4, 3, 4.

The pattern is - the number of 1's in the binary expansion of the positive integers starting from 1.

Number Binary Equivalent # of 1's

1 1 1
2 10 1
3 11 2
4 100 1
5 101 2
6 110 2
7 111 3
8 1000 1
9 1001 2
10 1010 2
11 1011 3
12 1100 2
13 1101 3
14 1110 3
15 1111 4
16 10000 1
17 10001 2
18 10010 2
19 10011 3
20 10100 2
21 10101 3
22 10110 3
23 10111 4
24 11000 2
25 11001 3
26 11010 3
27 11011 4
28 11100 3
29 11101 4

52. Substitute digits for the letters to make the following Division true

S T E M | D E M I S E

| D M O C



Note that the leftmost letter cant be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be 3?

C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9

It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).
S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T) must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).

Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.

O U T 4 1 3
------------- -------------
S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8

| D M O C | 9 5 4 0
------------- -------------
T U I S 3 1 6 2

S T E M 2 3 8 5
---------- ----------
Z Z Z E 7 7 7 8

Z U M M 7 1 5 5
-------- --------
I S T 6 2 3

Also, when arranged from 0 to 9, it spells CUSTOMIZED.

53. 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?

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.

54. Which number in the series does not fit in the given series:

1 4 3 16 6 36 7 64 9 100?

This is a series with odd positions containing position number whereas even positions containing square of the position.i.e. even position numbers are 4 16 36 64 100 and odd position numbers are 1 3 5 7 9

Hence, 6 does not fit in the series. It should be 5.

55. In the middle of the confounded desert, there is the lost city of "Ash". To reach it, I will have to travel overland by foot from the coast. On a trek like this, each person can only carry enough rations for five days and the farthest we can travel in one day is 30 miles. Also, the city is 120 miles from the starting point.
What I am trying to figure out is the fewest number of persons, including myself, that I will need in our Group so that I can reach the city, stay overnight, and then return to the coast without running out of supplies.

How many persons (including myself) will I need to accomplish this mission?

Total 4 persons (including you) required.

It is given that each person can only carry enough rations for five days. And there are 4 persons. Hence, total of 20 days rations is available.

1. First Day : 4 days of rations are used up. One person goes back using one day of rations for the return trip. The rations remaining for the further trek is for 15 days.

2. Second Day : The remaining three people use up 3 days of rations. One person goes back using 2 days of rations for the return trip. The rations remaining for the further trek is for 10 days.

3. Third Day : The remaining two people use up 2 days of rations. One person goes back using 3 days of rations for the return trip. The rations remaining for the further trek is for 5 days.

4. Fourth Day : The remaining person uses up one day of rations. He stays overnight. The next day he returns to the coast using 4 days of rations.

Thus, total 4 persons, including you are required.

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56. A goods can load wt only 100tones not more than that if inch more wt is added it will fall, So when the train was passing on the bridge a paper falls on it, Now will the train fall r not? if it doesnt fall why?

As the train had traveled a little bit distance to reach the bridge. hence the fuel has been reduced a little. thus the paper weight gets equated..

57. A series comprising of alphabets contains 13 letters. The first seven letters in the given series are A, E, F, H, I, L, M

Can you find the next two letters?

The next letters in the series are N, O, R, S, U, X.
The pattern is - letters whose English names (Phonetic Pronunciations) start with vowels.

58. 500 men are arranged in an array of 10 rows and 50 columns according to their heights.

Tallest among each row of all are asked to come out. And the shortest among them is A.
Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B.

Now who is taller A or B ?

No one is taller, both are same as A and B are the same person.

As it is mentioned that 500 men are arranged in an array of 10 rows and 50 columns according to their heights. Let's assume that position numbers represent their heights. Hence, the shortest among the 50, 100, 150, ... 450, 500 is person with height 50 i.e. A. Similarly the tallest among 1, 2, 3, 4, 5, ..... 48, 48, 50 is person with height 50 i.e. B

Now, both A and B are the person with height 50. Hence both are same.

In that question you mention 500 mens know then how will you say a&b both are persons
please clarify my doubt

59. A rich man died. In his will, he has divided his gold coins among his 5 sons, 5 daughters and a manager.

According to his will: First give one coin to manager. 1/5th of the remaining to the elder son. Now give one coin to the manager and 1/5th of the remaining to second son and so on..... After giving coins to 5th son, divided the remaining coins among five daughters equally.

All should get full coins. Find the minimum number of coins he has?

We tried to find out some simple mathematical method and finally we wrote small C program to find out the answer. The answer is 3121 coins.

Here is the breakup:

First son = 624 coins
Second son = 499 coins
Third son = 399 coins
Forth son = 319 coins
Fifth son = 255 coins
Daughters = 204 each

60. If you look at a clock and the time is 3:15.

What is the angle between the hour and the minute hands? ( The answer to this is not zero!)?

7.5 degrees

At 3:15 minute hand will be perfactly horizontal pointing towards 3. Whereas hour hand will be towards 4. Also, hour hand must have covered 1/4 of angle between 3 and 4.

The angle between two adjacent digits is 360/12 = 30 degrees.

Hence 1/4 of it is 7.5 degrees.

in a one minute minute hand travel six degree and in a one minute hour hand travel half degree.in a three o clock there is nienty degree angle so when minute hand travel ninty degree in 15 minute and hour hand also travel 7.5 degree.so there is 7.5 degree angle is formed.

61. Consider an n by n grid of squares. A square is said to be a neighbour of another one if it lies directly above/below or to its right/left. Thus, each square has at most four neighbours. Initially, some squares are marked. At successive clock ticks, an unmarked square marks itself if
at least two of its neighbours are marked. What is the minimum number of squares we need to mark initially so that all squares eventually get marked?

3 square marks initially at location (1,1), (1,2) and (2,1). Then it marks all square by considering atleast 2 marks square.

For an nxn grid of square, initially n squares should be marked in appropriate places so as to obtain solution....

Appropriate places should be chosen such that 2 initially marked squares should be neighbor of an unmarked square... Other initially marked squares should be placed such that, it should help in marking further squares...

62. A cricket team of 11 players lined up in a straight line to have their photograph. The captain was asked to stand in the center of the line-up.

1) Bharat and Bhavin stood to the right of the captain
2) Two players stood between Bhagat and Bhairav
3) Seven players stood between Bhadrik and Bhanu
4) Bhavesh stood to the right of Bhuvan
5) Bhola and Bhumit stood either side of Bhagat
6) Bhavik and Bhumit stood to the left of the captain
7) Six players stood between Bhavin and Bhagat
8 ) Two players stood between Bhagat and Bhavik

Who is the captain? Can you tell the positions of all the palyers?

Players from left to right : Bhavik, (Bhadrik/Bhanu), (Bhola/Bhumit), Bhagat, (Bhola/Bhumit), BHUVAN, Bhairav, (Bharat/Bhavesh), (Bharat/Bhavesh), (Bhadrik/Bhanu), Bhavin

Let's number the positions 1 to 11 from left to right. Hence, the captain is at position 6. Now, looking at the clues 7, 5, 2 and 8 together:

Poistion 1 - Bhavik or Bhairav
Position 3 - Bhumit or Bhola
Position 4 - Bhagat
Position 5 - Bhumit or Bhola
Poistion 7 - Bhavik or Bhairav
Position 11 - Bhavin

From clue (3), the only possible positions for Bhadrik and Bhanu are Position 2 and Position 10.

Now there are 3 positions remaining - 6, 8 and 9 and remaining 3 players are Bhuvan, Bharat and Bhavesh. But from clue (1), Bharat stood to the right of the captain i.e. Bharat must be on position 8 or 9 as position 6 is for the captain. So either Bhuvan or Bhavesh is the captain.

From (4), Bhavesh stood to the right of Bhuvan. Hence, Bhuvan is the captain.
Players from left to right are : Bhavik, (Bhadrik/Bhanu), (Bhola/Bhumit), Bhagat, (Bhola/Bhumit), BHUVAN, Bhairav, (Bharat/Bhavesh), (Bharat/Bhavesh), (Bhadrik/Bhanu), Bhavin.

* Bhavik(1), Bhagat(4), Bhuvan(6), Bhairav(7) and Bhavin(11) are the players whose positions are fixed.
* Bhadrik and Bhanu are at position 2 or 10.
* Bhola and Bhumit are at position 3 or 5.
* Bharat and Bhavesh are at position 8 or 9.

63. Substitute digits for the letters to make the following relation true.

+ W I T H I N

Note that the leftmost letter cant be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter S, no other letter can be 3 and all other S in the puzzle must be 3?

The value of L must be one more than W i.e. L=W+1 and there must be one carry from S+I=I. Also, the value of S must be 9 as S+I=I with one carry from T+T=M, which means that the value of T must be greater than 4.
From I+H=I, the value of H must be 0 as the value of S is 9.

Now, applying all those constraints and using trial-n-error, we get two possible answers.

9 7 1 6 6 9 8 5 3 3

+ 5 1 7 0 1 3 + 2 5 8 0 5 6
--------------- ---------------
6 1 4 1 7 9 3 5 6 5 8 9

The second answer

is wrong as the value of both N and M is 6 here.

I have tried all the combinations and there seems to be only one solution i.e. the first one
+ 97166

The other constraints that i have found while solving the question are :

L cant be 1
N cant be 8
H = 0
T can have only values 6/7/8
and corresponding M is 2/4/6