Important puzzles for Interview (Remaining will be added soon)

Puzzle 1 | (How to Measure 45 minutes using two identical wires?)

How do we measure forty-five minutes using two identical wires, each of which takes an hour to burn. We have matchsticks with us. The wires burn non-uniformly. So, for example, the two halves of a wire might burn in 10 minute and 50 minutes respectively

Solution :    

   

The wires are burning at non-uniform speed, but the time it takes to burn is uniform. The first wire when it is burning from both ends, it will take exactly 30mins to burn completely, but this point of both ends joining will not be the mid point.
Meanwhile, the one end which is burning in the second wire would have burnt for 30mins and then when lit from the other end, it will take exactly 15mins to burn completely.
So it total, you can measure 30 mins from 1st wire and 15mins from second wire and a total of 45 mins

Puzzle 2 | (Find ages of daughters)

Alok has three daughters. His friend Shyam wants to know the ages of his daughters. Alok gives him first hint.1) The product of their ages is 72.

Shyam says this is not enough information Alok gives him a second hint.

2) The sum of their ages is equal to my house number.

Shyam goes out and look at the house number and tells “I still do not have enough information to determine the ages”.

Alok admits that Shyam can not guess and gives him the third hint

3) The oldest of the girls likes strawbarry ice-cream.

Shyam is able to guess after the third hint. Can you guess what are the ages of three daughters?.

Solution :

1) Product of ages is 72

Below are all possibilities to get 72 from product of three different ages:

1 * 1 * 72 = 72

1 * 2 * 36 = 72

1 * 3 * 24 = 72

1 * 4 * 18 = 72

1 * 6 * 12 = 72

1 * 8 * 9 = 72

2 * 2 * 18 = 72

2 * 3 * 12 = 72

2 * 4 * 9 = 72

2 * 6 * 6 = 72

3 * 3 * 8 = 72

3 * 4 * 6 = 72

2) Sum of the ages is given

1 + 1 + 72 = 74

1 + 2 + 36 = 39

1 + 3 + 24 = 28

1 + 4 + 18 = 23

1 + 6 + 12 = 19

1 + 8 + 9 = 18

2 + 2 + 18 = 22

2 + 3 + 12 = 17

2 + 4 + 9 = 15

2 + 6 + 6 = 14

3 + 3 + 8 = 14

3 + 4 + 6 = 13

All sums are unique except 14. So the age sum must have been 14, otherwise Shyam would have guessed the ages from hint 1 only.

So we have two possible combination to get sum 14

2 + 6 + 6 = 14

3 + 3 + 8 = 14

3) Alok has an oldest girl (not two!!). So the ages must be 3, 3 and 8.

Puzzle 3 | (Calculate total distance travelled by bee)

Two trains are on same track and they are coming toward each other. The speed of first train is 50 KMs/h and the speed of second train is 70 KMs/h. A bee starts flying between the trains when the distance between two trains is 100 KMs. The bee first flies from first train to second train. Once it reaches the second train, it immediately flies back to the second train … and so on until trains collide. Calculate the total distance traveled by the bee. Speed of bee is 40 KMs/h.

Solution :

Let the first train moves at u km/h

second train moves at v km/h

distance betweem trains be d km

speed of bee is b km/h

time taken by trains to collide = d/(u+v)

distance travelled by bee = b*d/(u+v) = 40 * 100/(50+70) = 33.333

Puzzle 4 | (Pay an employee using a 7 units gold rod?)

An employee works for an employer for 7 days. The employer has a gold rod of 7 units. How does the employer pays to the employee so that the employee gets 1 unit at the end of everyday. The employer can make at most 2 cuts in rod.

 Solution:

Employer can pay for seven days by making 2 cuts in a way that he has 3 rods of size 1, 2 and 4.

1st Day: Employer gives 1 unit cut.

2nd day: Takes back 1 unit cut from employee given on first day and gives 2 unit cut.

3rd Day: Gives both 1 unit and 2 unit cuts.

4th Day: Takes back cuts of 1 and 2 units. Gives the cut of 4 units.

5th Day: Gives cut of 1 unit.

6th Day: Takes back cut of 1 unit and gives cut of 2 units.

7th Day: Gives cut of 1 unit.