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Information about 25 More selected Brain Teasers

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26. Five Hats Three smart kids A, B and C are shown a basket with 2 black and 3 white hats. They are blindfolded and a hat is placed on each kid’s head. They are then made to stand in a column with A in front, B behind him and C behind B. Then the blindfolds are removed, so that B can see A, C can see A and B, but A cannot see either B or C. They are then asked to guess the colour of the hat on their head. C has 1 min to answer, B has 2 mins and A has 3 mins to answer. After 1 min, C says, “I don’t know” After 2 mins, B says, “I don’t know” Before his time is up, A gives the correct answer. What is the colour of the hat on his head?

Three smart kids A, B and C are shown a basket with 2 black and 3 white hats. They are blindfolded and a hat is placed on each kid’s head. They are then made to stand in a column with A in front, B behind him and C behind B. Then the blindfolds are removed, so that B can see A, C can see A and B, but A cannot see either B or C. They are then asked to guess the colour of the hat on their head. C has 1 min to answer, B has 2 mins and A has 3 mins to answer.

After 1 min, C says, “I don’t know”

After 2 mins, B says, “I don’t know”

Before his time is up, A gives the correct answer. What is the colour of the hat on his head?

27. Dark one An African dressed in a black is crossing the road at place where there is no signal. A black car without headlights comes speeding on the road, but stops in time to let him pass. All the streetlamps are broken. There is no moonlight. How does the driver see the pedestrian? The time is midnight, by the way. (this variation to the classic puzzle was composed by SRG)

An African dressed in a black is crossing the road at place where there is no signal. A black car without headlights comes speeding on the road, but stops in time to let him pass. All the streetlamps are broken. There is no moonlight. How does the driver see the pedestrian? The time is midnight, by the way.

(this variation to the classic puzzle was composed by SRG)

Fun with Matchsticks 28. Arrange 8 matchsticks on a table as follows I - X = X I Moving only one matchstick make the two sides equal 29. Now solve the same problem without moving any matchstick.

30 & 31 30. A knockout tennis tournament had 171 contestants. If six balls were used in each match, how many balls were used till end of tournament. (there were no walkovers) 31.Father, Mother, son and Daughter need to cross a dark bridge. They have only one torch and only 2 persons can be at the bridge at any time. Mother can cross bridge in 10 mins, father in 5, Daughter in 2 and son in 1. What is the minimum time needed? (it is less than 18)

30. A knockout tennis tournament had 171 contestants. If six balls were used in each match, how many balls were used till end of tournament. (there were no walkovers)

31.Father, Mother, son and Daughter need to cross a dark bridge. They have only one torch and only 2 persons can be at the bridge at any time. Mother can cross bridge in 10 mins, father in 5, Daughter in 2 and son in 1. What is the minimum time needed? (it is less than 18)

32 - 33

34. Who is the engineer? On a train, Smith, Robinson and Jones are the fireman, brakeman and engineer, but NOT respectively. Also on the train are three businessman with the same names - Mr. Smith, Mr. Robinson and Mr. Jones. Using all the following clues find out who is the engineer. Mr. Robinson lives in Detroit The brakeman lives exactly half-way between Chicago and Detroit Mr. Jones earns exactly $ 20000 per year The Brakeman’s nearest neighbour, one of the passengers, earns exactly 3 times as much as the brakeman Smith beats the fireman at billiards The passenger whose name is the same as the Brakeman’s lives in Chicago

On a train, Smith, Robinson and Jones are the fireman, brakeman and engineer, but NOT respectively. Also on the train are three businessman with the same names - Mr. Smith, Mr. Robinson and Mr. Jones. Using all the following clues find out who is the engineer.

Mr. Robinson lives in Detroit

The brakeman lives exactly half-way between Chicago and Detroit

Mr. Jones earns exactly $ 20000 per year

The Brakeman’s nearest neighbour, one of the passengers, earns exactly 3 times as much as the brakeman

Smith beats the fireman at billiards

The passenger whose name is the same as the Brakeman’s lives in Chicago

35. The color of the ties Mr. White, Mr. Black and Mr. Grey once came to office wearing a white tie, a black tie and a grey tie. Did you notice, said Mr. Grey “ we are wearing ties that match our names, but none of us is wearing a ties with the same color as our name?”. “You are very observant, said the person with the black tie. Match the ties and names

Mr. White, Mr. Black and Mr. Grey once came to office wearing a white tie, a black tie and a grey tie. Did you notice, said Mr. Grey “ we are wearing ties that match our names, but none of us is wearing a ties with the same color as our name?”. “You are very observant, said the person with the black tie.

Match the ties and names

36. The classic matchstick puzzle Arrange 12 matchsticks in a square with 3 matchsticks to a side. If you consider each matchstick as one unit, the square has an area of nine square units. Now rearrange the matchsticks to enclose an area of 4 square units. All matchsticks must be used to form the perimeter and they cannot overlap or cross each other.

Arrange 12 matchsticks in a square with 3 matchsticks to a side. If you consider each matchstick as one unit, the square has an area of nine square units. Now rearrange the matchsticks to enclose an area of 4 square units. All matchsticks must be used to form the perimeter and they cannot overlap or cross each other.

37. One more distance problem A mile long column of soldiers led by a Major is marching at a uniform speed on a straight road. A soldier who is at the end of the column is asked to deliver a packet to the Major and return to his original position. He does so at a uniform speed. When he returns he discovers that the column has moved exactly one mile. How long did the messenger travel?

A mile long column of soldiers led by a Major is marching at a uniform speed on a straight road. A soldier who is at the end of the column is asked to deliver a packet to the Major and return to his original position. He does so at a uniform speed. When he returns he discovers that the column has moved exactly one mile. How long did the messenger travel?

38. Triangle Find angle X, using a simple construction. ( trigonometry not allowed)

Find angle X, using a simple construction.

( trigonometry not allowed)

39. Chess Four men - M1, M2, M3 and M4 and four ladies L1, L2, L3 and L4 are very fond of chess. One day after they had played one game each, it was observed that Though L2 and L3 both lost, ladies won more games than men M2 won his game, but M3 lost Who did M1 play with (puzzle composed by SRG )

Four men - M1, M2, M3 and M4 and four ladies L1, L2, L3 and L4 are very fond of chess. One day after they had played one game each, it was observed that

Though L2 and L3 both lost, ladies won more games than men

M2 won his game, but M3 lost Who did M1 play with

(puzzle composed by SRG )

40. Arrange 5 matchsticks to read: I I = V I Move one stick and make the sides equal 41. A clock takes 2 seconds to strike 2 Pm. How long does it take to strike 3 PM

42. Classic train problem Only the engine can pass under the bridge. All can go into the siding. Interchange A and B with E back in its original place.

Only the engine can pass under the bridge. All can go into the siding. Interchange A and B with E back in its original place.

43. Dividing the Herd A farmer has a herd with some cows and some horses. He has more than 4 sons, but no daughters. He issued following instructions for dividing the cows: First son can take as many cows as he can, such that his wife can take exactly 1/9 of what is left. The second son can take one more than the first and the wife gets exactly 1/9 of what is left. Third son gets one more than fourth, with the wife getting exactly 1/9 of what is left and so on. Each of them take cows in the above manner but the last son has no cows left for his wife. Then the farmer says - assume each horse equals two cows, distribute the horses so that each family gets an equal share of the herd. At least how many cows and horses were there in the herd? All results have to be in full units - no rounding off or cutting .

A farmer has a herd with some cows and some horses. He has more than 4 sons, but no daughters. He issued following instructions for dividing the cows:

First son can take as many cows as he can, such that his wife can take exactly 1/9 of what is left. The second son can take one more than the first and the wife gets exactly 1/9 of what is left. Third son gets one more than fourth, with the wife getting exactly 1/9 of what is left and so on. Each of them take cows in the above manner but the last son has no cows left for his wife. Then the farmer says - assume each horse equals two cows, distribute the horses so that each family gets an equal share of the herd.

At least how many cows and horses were there in the herd? All results have to be in full units - no rounding off or cutting .

44. Climbing Hemkund I climb Hemkund peak starting at 6 am in the morning. I climb at a uniform speed but take a break from time to time and reach Hemkund after 2 Pm. Next morning I climb down the hill at a uniformly faster speed, but again taking breaks from time to time. Is there one place in the hill where I was at the same time on both days?

I climb Hemkund peak starting at 6 am in the morning. I climb at a uniform speed but take a break from time to time and reach Hemkund after 2 Pm. Next morning I climb down the hill at a uniformly faster speed, but again taking breaks from time to time. Is there one place in the hill where I was at the same time on both days?

45. Mathematical family The mother is 3 times as old as the daughter was when the father is the same age as the mother is now. When the daughter reaches the same age as the mother is now, the son will be half as old as the father was when the mother was twice the age the daughter is now. When the father reaches twice the age the mother was when the daughter was the same age as the son is now, the daughter will be 4 times as old as the son is now. Given that one of their ages is a perfect square, what are the four ages? All numbers are integral

The mother is 3 times as old as the daughter was when the father is the same age as the mother is now. When the daughter reaches the same age as the mother is now, the son will be half as old as the father was when the mother was twice the age the daughter is now. When the father reaches twice the age the mother was when the daughter was the same age as the son is now, the daughter will be 4 times as old as the son is now. Given that one of their ages is a perfect square, what are the four ages? All numbers are integral

46. All squares From a square 8 Cms X 8 Cms, two squares are cut from diagonally opposite corners of 1 cm X 1 cm. If you are given 31 rectangular strips of 2cms X 1 cm is it possible to exactly cover the remaining part.

From a square 8 Cms X 8 Cms, two squares are cut from diagonally opposite corners of 1 cm X 1 cm. If you are given 31 rectangular strips of 2cms X 1 cm is it possible to exactly cover the remaining part.

47. Another Train problem Interchange A and B. A and B are each 10 feet long. E = 15 feet. Left siding is 10 feet, right siding is 25 feet. Top siding is very long.

Interchange A and B. A and B are each 10 feet long. E = 15 feet. Left siding is 10 feet, right siding is 25 feet. Top siding is very long.

48. Girlfriends A man staying in Dadar (Mumbai) has a girlfriend each in VT and Thane. (VT and Thane are in opposite directions) Frequency of trains towards VT from Dadar is one every 10 mins. Same is the frequency of trains towards Thane from Dadar. Each morning the man reaches the station at a random time and takes the first train going in either direction. Yet he meets the VT girlfriend 4 times as much as the Thane girlfriend. Why?

A man staying in Dadar (Mumbai) has a girlfriend each in VT and Thane. (VT and Thane are in opposite directions) Frequency of trains towards VT from Dadar is one every 10 mins. Same is the frequency of trains towards Thane from Dadar. Each morning the man reaches the station at a random time and takes the first train going in either direction. Yet he meets the VT girlfriend 4 times as much as the Thane girlfriend. Why?

49. Acrobat There are two ropes hanging from a rod near the ceiling at a height of 14 feet which are approximately 30 cms apart. The ropes reach the floor. An acrobat 5 feet tall, armed with a knife has to cut as much of the two ropes as possible. He dies if he falls. What method will he adopt to retrieve that maximum length?

There are two ropes hanging from a rod near the ceiling at a height of 14 feet which are approximately 30 cms apart. The ropes reach the floor. An acrobat 5 feet tall, armed with a knife has to cut as much of the two ropes as possible. He dies if he falls. What method will he adopt to retrieve that maximum length?

50.Smart hostess An airline company has three planes each with a capacity of 36 and two toilets at the rear. The air hostess has the responsibility of doing a count of passengers before take off. One day, all the aircrafts take off with the same number of passengers, but one of the three hostesses finishes her count in about half the time it takes each of her colleagues. What was the number of passengers flying. (Composed by SRG)

An airline company has three planes each with a capacity of 36 and two toilets at the rear. The air hostess has the responsibility of doing a count of passengers before take off. One day, all the aircrafts take off with the same number of passengers, but one of the three hostesses finishes her count in about half the time it takes each of her colleagues. What was the number of passengers flying.

(Composed by SRG)

Answers 26-39 26. White. If C had seen Black on both A and B, he would have answered “White”. Knowing the C did not see Black and Black, if B had seen Black on A’s head, he would have answered Black. Since B also did not answer, A had to have White on his head. 27. This happened in Finland, land of the Midnight Sun during one of the 24 hour sunlight days 28. I X = X – I : 29. View the matchsticks from the other side – X = X - I 30. 170 players have to be eliminated, so 170X6 balls are needed 31. 17. son+daughter(2), Son back (1), father +mother (10), daughter back (2), son + daughter (2) 32. The others were women 33. He was a lighthouse keeper 34. Smith. Brakeman’s neighbor is not Mr. Robinson or Mr. Jones, so he is Mr. Smith. The passenger whose name is same as the brakeman lives in Chicago, so he is not Mr. Robinson or Mr. Smith. So he is Mr. Jones. Smith beats the fireman at billiards so Fireman must be Robinson. 35. Since Mr. Grey does not wear grey or black, he wears white. So Mr. Black wears Grey and Mr. White wears black 36. First form a triangle with 6 sticks as the hypotenuse and 3 sticks on each side. Area of this triangle is 6 units. Then move the 3 matches from the right angle inside to form a rectangular shape that reduces exactly 2 units. 37. 1+ square root of 2 38. Let F be on AD such that FCD=20degrees. Then BC=CD=CF= BF=EF. Thus BEF=70 degrees and BEC = 30degrees 39. There were at least 3 games which were not drawn, so ladies won two games, men one and the third was a draw. Ladies won two and lost two, so none were involved in a draw. M2 won, M3 lost. So M1 played M4 to a draw.

26. White. If C had seen Black on both A and B, he would have answered “White”. Knowing the C did not see Black and Black, if B had seen Black on A’s head, he would have answered Black. Since B also did not answer, A had to have White on his head.

27. This happened in Finland, land of the Midnight Sun during one of the 24 hour sunlight days

28. I X = X – I : 29. View the matchsticks from the other side – X = X - I

30. 170 players have to be eliminated, so 170X6 balls are needed

31. 17. son+daughter(2), Son back (1), father +mother (10), daughter back (2), son + daughter (2)

32. The others were women 33. He was a lighthouse keeper

34. Smith. Brakeman’s neighbor is not Mr. Robinson or Mr. Jones, so he is Mr. Smith. The passenger whose name is same as the brakeman lives in Chicago, so he is not Mr. Robinson or Mr. Smith. So he is Mr. Jones. Smith beats the fireman at billiards so Fireman must be Robinson.

35. Since Mr. Grey does not wear grey or black, he wears white. So Mr. Black wears Grey and Mr. White wears black

36. First form a triangle with 6 sticks as the hypotenuse and 3 sticks on each side. Area of this triangle is 6 units. Then move the 3 matches from the right angle inside to form a rectangular shape that reduces exactly 2 units.

37. 1+ square root of 2

38. Let F be on AD such that FCD=20degrees. Then BC=CD=CF= BF=EF. Thus BEF=70 degrees and BEC = 30degrees

39. There were at least 3 games which were not drawn, so ladies won two games, men one and the third was a draw. Ladies won two and lost two, so none were involved in a draw. M2 won, M3 lost. So M1 played M4 to a draw.

Answers 40-50 40. I = Square root of I ; 41. 4 seconds. Each chime is after a 2 second gap 42. Move B to siding. Go over bridge and connect A to B. Move B back to old position and A to siding. Going over the bridge move B to left. Get A from siding and move it to right, Come back to siding. 43. 56 cows and 8 horses. Each family gets one horse and 8 cows. There are 7 sons. Hint - start with the last son and work backwards. The lowest possible number for him is 8 with his elder brother’s wife getting 1 out of 9 cows, leaving 8 for him. Each family gets 8 cows and 8 horses. 44. Yes. Imagine two persons starting from opposite directions at the same time. They would meet at some point. 45. Son 12, Daughter 16, Mother 42, Father 44. Hint – Solve the foll. equations: 3F-2M-3D=0; F-2M+4D-2S=0 F-2M+d+2s=0 46. N0. Imagine a chess board of 64 squares. The diagonally opposite squares have the same color. Each 2X1 rectangle covers one black and one white square. So it is not possible to cover the remaining area exactly 47. DIY 48. Trains to VT are at 1000, 1010 1020 and so on. Trains to Thane are at 1002, 1012, 1022 and so on. For every 8 minute period when he will catch a VT train, he will catch a Thane train in a 2 min period. 49. Ties the ropes at the bottom. Climbs to the top, hangs on the rod, cuts the ropes at the top and loops the rope over the rod, then climbs down holding both ropes. This way he retrieves all the rope. 50. 24. The smart hostess counted the number of empty seats. So one third was empty.

40. I = Square root of I ; 41. 4 seconds. Each chime is after a 2 second gap

42. Move B to siding. Go over bridge and connect A to B. Move B back to old position and A to siding. Going over the bridge move B to left. Get A from siding and move it to right, Come back to siding.

43. 56 cows and 8 horses. Each family gets one horse and 8 cows. There are 7 sons. Hint - start with the last son and work backwards. The lowest possible number for him is 8 with his elder brother’s wife getting 1 out of 9 cows, leaving 8 for him. Each family gets 8 cows and 8 horses.

44. Yes. Imagine two persons starting from opposite directions at the same time. They would meet at some point.

45. Son 12, Daughter 16, Mother 42, Father 44. Hint – Solve the foll. equations: 3F-2M-3D=0; F-2M+4D-2S=0 F-2M+d+2s=0

46. N0. Imagine a chess board of 64 squares. The diagonally opposite squares have the same color. Each 2X1 rectangle covers one black and one white square. So it is not possible to cover the remaining area exactly

47. DIY

48. Trains to VT are at 1000, 1010 1020 and so on. Trains to Thane are at 1002, 1012, 1022 and so on. For every 8 minute period when he will catch a VT train, he will catch a Thane train in a 2 min period.

49. Ties the ropes at the bottom. Climbs to the top, hangs on the rod, cuts the ropes at the top and loops the rope over the rod, then climbs down holding both ropes. This way he retrieves all the rope.

50. 24. The smart hostess counted the number of empty seats. So one third was empty.

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