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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
At the grand ball dance thrown by the king, on the eve of the prince's wedding, each guest was asked to dance with any other partner, excluding his/her spouse. The pair could be formed between a man and a man, woman and a woman, man and a woman amongst the 20 couples who were invitees to the function and no partner could be repeated. At the end of the dance, the King was very curious to know the number of people, each invitee had danced with. So he asked everyone, to say aloud the number of people he/she had danced with and received 39 distinct replies. Mr. Beckham said he had danced with 38 people. Can you tell me how many people did Mrs. Beckham dance with?
Answer 
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.
One evening you are sitting in a room with no windows and the door shut. Suddenly you hear two cars drive up outside. From the noise of the engines you can make out that one car's engine is well tuned, whereas the other car's engine is in urgent need of repair. The engines are switched off and you are asked to go out and identify the car with the good engine. You are allowed to start only one engine to hear the noise. However, when you get outside, you find 3 cars. You are told that one of them was already there for a long time. How can you be sure to find the car with the good engine?
Answer
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.
An old lady had packed all her jewels in one box and wanted to send it to her grand-daughter. The lady possessed many locks and their keys but her grand-daughter had no copies of the keys. Although the jewel-box had facility for multiple locks, she could not parcel the key(s) to her grand-daughter for fear of it being intercepted. How could the lady send her jewels securely to her grand-daughter?
Answer
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.
During the screening test for enrollment in an MBA program, each of the short-listed candidates had to individually face the following exam in order to qualify for the next round.
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?
Answer
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).
A thief was caught and sentenced to death by the king. However, as a tradition of the land, each criminal could choose the way he would like to kiss death. But this thief was very cunning, can you tell me, what did he choose?
Answer
The thief chose natural death.
At a game show, George was given 3 wax sticks with a wick running along its length, each of which would take 2 hrs to burn, if lit at one end. The sticks were uneven in dimension (that is thicker at some places compared to the rest of the rope), hence if you cut the stick into two equal pieces you cannot assume that it would take one hour for them to burn.
George was told to use the sticks to measure 2½ hours. What did he do?
Answer
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.]
An affluent landlord needed to pay his gardener for revamping his garden, which would demand a week's hard work. But as he was short of cash, he decided that he would pay the gardener one ring each day, from a 7 link long gold chain that he possessed.
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?
Answer
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.
You have four 9's and you may use any of the following operations (+, -, /, *) as many times as you like. You have to create a mathematical expression which uses exactly four 9's to give a result of 100.
How many such expressions can you make and what are they?
Answer
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
At a conference, 12 members shook hands with each other before & after the meeting. How many total number of hand shakes occurred?
Answer
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.
A milkman has a can of 20 gallons, full of milk. But due to a sudden epidemic, all his cows in the farm fall sick. He can no longer collect milk from them.
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?
Answer
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.
A safe of a treasure chest can be unlocked with a 5 digit key. The following is known about it. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11. Find the number.
Answer
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.
Out of the 70 employees working with ABC Inc., 30 are females. Also,
- 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
Answer
15 un-promoted females & none are above 30 years of age.
Simply putting all given information into the table structure, we get the answer.
As per the will of a late farmer, his property would have to be divided in the following way. The eldest got half of the land and an added 2 acres. Second son received of the remaining land plus 2 acres. Third son got half of the remaining +2 acres. But as the fourth son took half of the remaining plus 2 acres of land, there was nothing left for the fifth son. How many acres of land did the farmer originally have?
Answer
The farmer originally owned 60 acres of land.
Let the original amount of land be x acres.
1st son got x⁄2 +2 = (x+4)⁄2
Land remaining = x - (x+4)⁄2 = (x-4)⁄2
2nd 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
Ms. Janette takes a train to her granny's place. While on her journey she falls asleep when the train still has twice as far to go as it has already gone.
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?
Answer
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
The workforce of a firm is divided into 4 groups for allocation to different projects. Each group is a motley of Managers, Technicians and Executives.
- 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?
Answer
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