# Puzzles and Brain Teasers

Brain teasers and puzzles help you to train your brain. So go ahead, take our Brain Teaser. And don't take a peek at the answer until you have tried really hard.## Brain Teasers and Puzzles

Can you tell us Ben's reply, as his answer impressed the examiner and he was selected for admission to that Business school?

- What place did Steve achieve after overtaking his friend?
- What place would Steve have achieved had he managed to overtake the last runner?

- Steve stood second by overtaking the second runner and not first which is a common mistake made by most of us.
- How can one overtake the last runner?

Both the trains are equidistant from New York at the meeting point. The distance of the meeting point from New York will obviously be the same for both trains.

Nancy had 4 flowers and 3 vases.

Let x be the number of flowers, and y be the number of vases.

x - y = 1

or

y = x - 1

From the statement "if she put two flowers per vase, she had one vase empty", we get:

2 (y - 1) = x

or

2 (x - 1 - 1) = x (putting the value of y from equation 1)

or

2x - 2 - 2 = x

or

2x - x = 4

or

x = 4

Hence, y = 3

Thus, Nancy had 4 flowers and 3 vases.

The match.

Without lighting the match you cannot light any of the others.

Rachel takes one light out from the box which is labeled 'Blue and Red'. If it is a blue light, then this is the box which contains only blue lights, since the only other box that can contain blue lights is the one which has both blue and red lights. However, this cannot be that box since it already had the label 'Blue and Red' which we know is incorrect.

This means that the box marked 'Blue' actually contains red balls. This is because the only other box that remains is already marked 'Red' which we know is incorrect. This also means that the box marked 'Red' would contain both blue and red balls.

Had Rachel picked out a red light from the first box, then similar reasoning would lead us to the correct results.

When she left home, the hour hand and the minute hand were cast exactly opposite each other and on reaching school she found them to be together.

Similarly, when she quit school in the evening, the hour hand and the minute hand were together and the moment she arrived home, they were exactly opposite each other.

How much time did Mrs. Benette spend traveling? Give the minimal possible answer.

1 hr, 5 mins and 27.2 secs.

The minute hand and the hour hand are together 11 times, in twelve hours,. It means that after every 12/11 hours, both the hands are together.

Similarly, the minute hand and the hour hand are exactly opposite to each other 11 times, in twelve hours. It means that after every 12/11 hours, both the hands are opposite each other.We know that at 12:00 both the hands are together and at 6:00 both the hands are exactly opposite to each other.

After 6:00, both the hands are in opposition at [6+(12/11)] hours, [6+2*(12/11)] hours, [6+3*(12/11)] hours and so on. The sixth such time is [6+6*(12/11)] hours, which is the first time after 12:00. Thus after 12:00, both the hands are opposite to each other at 12:32:43.6.

Hence, Mrs. Benette takes 32 minutes and 43.6 seconds to reach home from school. Her total travel time is twice of this time, which equals to 1hr, 5mins and 27.2 secs.

Thus the photographer asked his driver to visit the nearest forest officer's home and inquire the time. The driver drove the jeep at a constant speed to the forest officer's place, asked him the time, rested there for 5 mins and drove back to the jungle at the same speed at which he had gone. On the driver's arrival the photographer could set the right time on his watch. Can you tell me how?

Note - The driver did not have his own watch and neither did the forest office have a spare one which he could lend to the driver to take back with him.

Assume that when the driver left, the photographer had tuned his watch to a random time of 12:00 hrs.

Let the total travel time of the driver be 2t, as he drove with the same speed on his forward and backward journey.

On the driver's return, the photographer's watch read (12 + 5/60 + 2t). From this he could find out the value of t. The driver's journey from the time he quit the forest officer's home was T+t ( T being the time the driver noted while setting back for the jungle from the forest officer.) Since both the quantities are known the correct time could be determined.

Mrs. Beckham had danced with 0 person.

20 couples implied 40 people at the ball. No one was allowed to dance with his/her own spouse. No person danced with himself/herself or his/her spouse. Thus the maximum number of persons he/she could dance with is 40-2 = 38.

The problem says this person is Mr. Beckham. 39 distinct replies means 0,1,2,3,4.....38, plus one number that lies within this range. Since there are only 38 other invitees apart from Mr. Beckham and his wife, each one of the rest must have danced with at least one person. This leaves only the number '0', which is the number of person Mrs. Beckham danced with.

The engines of the two cars which just arrived would be a lot warmer than the one which had been there for a long time. Hence I simply touch the hood of the cars and identify the two which just arrived. I then sit in any one and start the engine. If the noise is of the engine needing urgent repair then the car with the good engine is the other warm car. If not, then I am sitting in the car with the good engine.

The lady would first lock the box with her own lock and send it to her grand-daughter without any key. The grand-daughter could then fix one of her own locks, whose key she possessed, onto the box and mail it back to her grand-mother. The lady would then remove her own lock and send the box back to her grand-daughter. The grand-daughter could then unlock her own lock and receive the jewels.

There were two rooms, one of which had 100 light bulbs, and the other contained their corresponding switches. Which switch belonged to which bulb was not known. The candidates were told that out of the 100 bulbs, 30 of them were glowing, while the rest were not. There was no way to tell whether the switches were in 'on' or 'off' state by just looking at them. A candidate was allowed to move between the rooms but could not see one room from the other. He was required to divide the switches into 2 groups such that each of them contained equal number of corresponding lighted bulbs. Toggling the switches would change the state of the corresponding bulb.

Could you help them devise a strategy?

A candidate would have to select 30 switches randomly from the collection and name it Group 1. Assume it had 'z' number of 'on' bulbs. Now the remaining switches which formed Group 2 had (30 - z) number of 'on' bulbs, since z + (30 - z) = 30. Now if he flipped all the switches of Group 1, the number of lighted bulbs would become (30 - z), which would be the same as the number of lighted bulbs in Group 2, i.e (30 - z).

The thief chose natural death.

George was told to use the sticks to measure 2½ hours. What did he do?

Firstly, he set fire to both ends of the first stick, which took an hour to burn (as it was burning with twice the rate.) [Count 1 hour].

As soon as it finished burning, he set fire to both ends of the second stick and one end of the third stick simultaneously; the second stick took another one hour to burn [Count 2 hours].

As soon as the second stick has burned off, George lit the other end too, of the third stick. As this stick had already burned for one hour already, with one hour remaining, it took half an hour to burn the remaining half. [Count 2½ hours.]

But the landlord did not want to make too many cuts in the chain as he wanted it back, once he had the cash to pay the gardener. What is the minimum number of cuts that the landlord needs to make in his chain?

The landlord needs to make only one cut on the third link, setting it free from both sides of the adjoining parts of the chain. This would result in 3 pieces:

1. 1 link (that was cut.)

2. 2 links joined together and

3. 4 links joined together.

Day1. Give the single cut link.

Day2. Give the piece with 2 links and take back previous day's link.

Day3. Give the single link.

Day4. Give the piece with four links and take back the pieces with 1 and 2 links.

Day5. Give the single link.

Day6. Give the piece with 2 links and take back the single link.

Day7. Give the single link.

How many such expressions can you make and what are they?

There are 5 such expressions:

99 + (9/9) = 100

(99/.99) = 100

(9/.9) X (9/.9) = 100

((9*9) + 9)/.9 = 100

(99-9)/.9 = 100

132

The first person shook hands with 11 remaining people, the second person also shook hands with 11 people, but we count 10, as the hand shake with the first person has already been counted. Then add 9 for the third person, 8 for the fourth one & proceeding in this fashion we get:

11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66

66 hand shakes took place before & 66 after the meeting, for a total of 132.

To conserve his milk he decides that on the first day he will sell one liter and refill the can back with water. On the 2nd day he will take out 2 liters and refill the bottle. On the 3rd day he will take out 3liters and so on...

By the time all the milk is gone, how much water has the milkman sold?

The milkman has sold 190 liters of water.

It is given that the milkman had a 20 liters can of milk. From the first day, when he sold 1 liter of milk, until the end of 20 days, he must have sold

(1 + 2 + 3 + 4 + ..... +18 + 19 + 20) = 210 liters of adulterated milk.

Out of that 210 liters, 20 liters was pure milk which he had initially. Hence, he must have sold

(210 - 20) = 190 liters of water.

65292

As per given conditions, there are three possible combinations for 2nd, 3rd and 4th digits. They are:

3, 0, 7 or

4, 1, 8 or

5, 2, 9

It is given that there are 3 pairs whose sum is 11. All possible pairs are

2, 9

3, 8

4, 7

5, 6

Now required number is 5 digit number and it contains 3 pairs of 11. So it must not be having 0 and 1 in it.

Hence, the only possible combination for 2nd, 3rd and 4th digits is

5, 2, 9

Also, the 1st digit is thrice the last digit. The possible combinations are

3, 1

6, 2

9, 3

Out of these only (6, 2) with (5, 2, 9) gives 3 pairs of 11. Hence, the answer is 65292.

- 30 employees received a promotion
- 24 employees are above 30 years of age
- 19, amongst the promoted employees are over 30 years, of which 7 are males
- 12 males are above 30 years of age
- 15 males have received a promotion

15 un-promoted females & none are above 30 years of age.

Simply putting all given information into the table structure, we get the answer.

The farmer originally owned 60 acres of land.

Let the original amount of land be x acres.

1^{st} son got ^{x}⁄_{2} +2 = ^{(x+4)}⁄_{2}

Land remaining = x - ^{(x+4)}⁄_{2} = ^{(x-4)}⁄_{2}

2^{nd} son got {^{(x+4)}⁄_{4} + 2}

Proceeding like this, what remain after 4th son gets his share is ^{(x-60)}⁄_{16}

This obviously equates to 0, as there is nothing left for 5th son.

x - 60 = 0

Hence, x = 60

Halfway through the trip she wakes up when the train stops at a signal. When she finally falls asleep again, the train has yet half the distance to go that it has already traveled. Fortunately, Ms. Janette wakes up at the end of her trip.

What fraction of the total trip did Ms. Janette travel sleeping?

Ms. Janette slept through half her trip.

Let's draw a timeline. Picture the train route on a line shown below:

----- shows time for which Ms. Janette was not sleeping

___shows time for which Ms. Janette was sleeping

Adding up, all sleeping times,
= (½ - ⅓) + (1 - ⅔)

= ⅙ + ⅓

= ½

- Group I : 1 Manager, 1 Technician and 1 Executive
- Group II : 1 Manager, 5 Technicians and 7 Executives
- Group III : 1 Manager, 7 Technicians and 10 Executives
- Group IV : 9 Managers, 23 Technicians and 30 Executives

The cumulative wage of all the members of Group II costs $300 and that of Group III members costs $390. Can you calculate, what wage expense the Company bears for Group I and Group IV members?

Group I wage is $120 and Group IV wage is $1710

Assume that the wages of a managers, a technician and an executive are M,T and E respectively.

For Group II : M + 5T + 7E = 300 .....(i)

For Group III : M + 7T + 10E = 390...(ii)

Subtracting equation (ii) from (i) : 2T + 3B = 90

For Group I:
= M + T + B

= (M + 5T + 7E) - (4T + 6E)

= (M + 5T + 7E) - 2(2T + 3E)

= 300 - 2(90)

= 300 - 180

= 120

Similarly, for Group IV:
= 9M + 23T + 30E

= 9(M + 5T + 7E) - (22T + 33E)

= 9(M + 5T + 7 E) - 11(2T + 3E)

= 9(300) - 11(90)

= 2700 - 990

= 1710

- How many flowers did she deposit in each church?
- What is the least number of flowers Mrs. Benette must have had initially to make the above possible?

Mrs. Benette deposited 16 Easter Lilies at each church and she had originally brought 15 of them.

Lets say Mrs. Bennette had x flowers with her initially.

When she washed them in the lake, they doubled in no. hence she had 2x flowers.

She deposited y (say) flowers in the first church and came out with 2x-y flowers.

She washed them in the lake waters and had 2(2x - y) flowers.

She entered 2nd church with 2(2x - y) flowers = 4x - 2y

She came out with (4x - 2y ) - y flowers = 4x - 3y

She entered 3rd church with 2(4x - 3y) flowers = 8x - 6y

She came out with (8x - 6y)- y flowers = 8x - 7y

She entered 4th church with 2(8x - 7y) flowers = 16x - 14y

And deposited all of them there, hence

16x - 14y = y

Or, 16x =15y

Since we are interested in the least possible x,
x=15

y=16

How?

Quite simple. I got down from my car, and handed the keys to my friend, asking him to drive the old lady to the hospital; while I waited with the girl of my dreams for the bus.

- No two residents have exactly the same income.
- No resident's income exactly amounts to $3055.
- The number of residents outnumbers the income of individual residents.

What is the largest possible population strength of the city of Wonderland?

3055.

It is given that no resident's income exactly amounts to $3055.

Hence there are 3055 residents with their income ranging from $0 to $3054. Assuming more than 3055 residents will violate the 3rd condition.

As for any number exceeding 3055, there will be same number of residents as the income of highest earning resident.

The following information about their choice was supplied:

- Antonio said either Bambino or Jackie will definitely win.
- Harry said he is confident that Bambino will not win.
- James said he is confident that neither Jackie nor Lexus will win.

When the results were out, it was found that only one of the above three had made a correct statement. Can you tell who has made the correct statement and who has won the contest?

Harry; Lexus.

If Antonio is correct, then either of Harry or James will be correct depending on whether Bambino or Jackie win the race. This directly contradicts the given argument that only one of the bidder's statements is true. Similar is the case with James.

However if Harry's statement is held true, then, both Antonio and James's statements will automatically be false, if we reason out the winner to be Lexus.

The following information about their choice was supplied:

- The routes were The North Road, South Road, East Road and West Road.
- None of the travelers took the road which was their namesake.
- Mr. East did not take the South Road.
- Mr. West did not the South Road.
- The West Road was not taken by Mr. East.

Can you tell which road did each traveler take?

- Since Mr. East cannot take South Road and West Road (given) and East Road (because it is his namesake), he obviously chose the North Road.
- Mr. West did not take the South Road (given) and not the West Road (because it is his namesake) hence he must have taken the East Road.
- Mr. West did not take the South Road (because it is his namesake), hence he must have taken West Road.
- Finally, we are left with Mr. North who must have taken the South Road.

- George is a widower and lives alone with his only daughter who takes care of him.
- Michael is a bachelor and his niece cooks for him and looks after his house.
- Robert is married to a charming lady called Christina and they live together in a large apartment in the same town.

Christina suggests that all of them could stay together in a single house and share monthly expenses equally. During their first month of living together, each person contributed $1025. At the end of the month, it was found that $4068 was the total expense so the remaining amount was distributed equally among everyone. The distribution was such that everyone received $8 each. How do you explain the situation?

George's daughter, Michael's niece and Robert's wife are one and the same person - Christina.

According to the problem,

Total contribution = 1025 x 4 = $4100

Total expenditure = $4068

Therefore amount remaining = $4100 - $4068= $32

Each person received $8

Hence there are $32/$8 = 4 persons

They are:

- George
- Michael
- Robert
- Christina

The pots of the tallest plants among each row of all are painted pink. And the shortest among them is painted red.

Similarly, the pots of the shortest plants among each column are painted yellow. And the tallest amongst them is painted orange.

Now can you tell which pot has the taller plant, the red pot or the orange one?

In both the situations, plant X50_{1} satisfies the condition. Thus the red and orange painted pots actually refer to the same plant.

As per the puzzle, 500 plants were arranged in order of their height (say, ascending order of their height). Diagrammatically, it can be represented as:

X10_{10}.......................X50_{10}

X9_{9}...........................X50_{9}

X8_{8}...........................X50_{8}

.

.

.

.

X1_{1}.......................X50_{1}

The plant positioned in the last position of the last column (X5010) is the tallest amongst all plants and the plant posted on the first position of the first column (X1_{1})is the shortest amongst all.