Three Friends Puzzle Solution

In this puzzle we have to make sure that no person is in danger.

Let the names of the persons be A, B and C.

So they start from their starting point and after 1st day A give it's 2 days resource to B and C. So A has 1 day resource left with him which he can use to return back to the starting point. Now B and C starts again and they have a 4 day supply again because of the food and water given by A.

After the second day B gives his 1 day supply to C and keeps the remaining 2 days supply with him so that he can return safely to the starting point.

Now after 2nd day C again has 4 days supply so he can continue towards the destination point and will reach there safely.

So only 1 person can reach the destination safely.

Images:

A - 4 days                                                                                                                  A - 3 days
B - 4 days  ----------------------------------------------------------------------------------- B - 3 days
C - 4 days                                           after 1st day                                                  C - 3days

A gave its 2 days supply to B and C. So now

A - 1 day                                                                                                                                
B - 4 days  ---------------------------------------------------------------------------------- B - 3 days
C - 4 days                                           after 2nd day                                                 C - 3days

B gave it's 1 day supply to C and B returns back.
B - 2 days
C - 4 days

So C has 4 days resources and can cover the 4 remaining days.

Three Friends Puzzle

This puzzles is used to test the management capability of the student by the interviewers.

Three Friends starts on a trip to the Sahara Desert. It takes 6 days to reach the destination. Each person can carry only enough food and water for 4 days. So the maximum resource which a person can carry will last for 4 days.

There is no place in between the trip where they can refill their resources.

Without risking anyone's life they have to make as many people as possible to safely reach the destination. How many people can safely reach the destination.?

Click here for the solution

Daughters Age Puzzle Solution

Well this puzzles looks very vague the first time you listen to it. But if you understand each and every word of it you will figure out the solution.

Let's start with all the combinations possible as we know that the product of their ages is 72.

Ages                                                                                     Sum

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

After looking at the building number Scientist 1 is not able to figure out what are the ages of the daughters.
So if we look at the sample space shown above we will find that there are two cases. This means that the number on the building was 14 and the Scientist 1 is confused with 3,3,8 and 2,6,6 as options.

Since Scientist 2 says that the older daughter plays piano. This means that the 2,6,6 possibility is gone so the ages of the daughters are 3,3,8.

Everything is mentioned in the puzzles. Just you have to think and try to figure out the solution.

Daughters Age Puzzle

This Puzzle involves a bit of mathematics to figure out the correct solution.

Two Scientist met each other after twenty years.
Scientist 1: How are you?
Scientist 2: Great. I got marries and have 3 daughters now.
Scientist 1: That's really great. How old are they?
Scientist 2: Well the product of their ages is 72 and the sum of their ages is the number written on that building.
Scientist 1: ok I go it. Wait still i am not clear.
Scientist 2: Ohh sorry the oldest one has just started to play piano.
Scientist 1: Wonderful my oldest daughter is of the same age.

How old are the daughters and how does scientist 1 find this?

Click here for the Solution

Sand Timers Puzzle Solution

The solution is simple as you have to think in the right direction.

Start both the sand timers together. Once the 7 minutes are over sand in the 7 minute timer will be completed moved from one portion to the other. Reverse the 7 minutes timer and wait.

When the 11 minutes sand timer gets finished reverse the 7 minutes timer again and wait for it to finish transferring the sand from one portion to another. It will take 4 minutes and in total you can measure 15 minutes.

Mathematically

7 Minutes Sand Timer Finished.

Time Remaining in 11 minutes timer - 4 minutes

Reversing the 7 minutes timer - 4 minutes will elapse.

Once 11 minutes gets over reverse the 7 minutes timer again to use that 4 minutes

So total = 7+4+4 = 15 minutes.

Sand Timers Puzzle

This Puzzle is one of the most commonly asked interview Puzzles and most of the time students are not able to answer it correctly.

You have two sand timers with you. One can measure 7 minutes and the other sand timer can measure 11 minutes. This means that it takes 7 minutes for the sand timer to completely empty the sand from one portion to the other.

You have to measure 15 minutes using both the timers. How will you measure it.

Click  Here for the Solution

River Crossing Puzzle Solution

The trick to this puzzle is that you can keep fox and grain together. So the solution would be

The man will start with the chicken. He will go to the other side of the river with the chicken. He will keep chicken there and will return back and will take grain with him on the next turn. When he reaches the other side he will keep the grain there and will take chicken back with him.

Now we will take fox and will keep the fox at the other side of the river along with the grain. He will return back and will take chicken along with him. This way they all will cross the river.

Just to give a clear picture

M - Man
C- Chicken
F- Fox
G- Grain

M C F G ------------------------------------------------------------------------------- other side

F G ------------------------------------------------------------------------------------- M C

Man return back

F G M ---------------------------------------------------------------------------------- C

F ----------------------------------------------------------------------------------------G M C

Man returns back with Chicken

F C M ----------------------------------------------------------------------------------- G

Takes Fox with him

C ---------------------------------------------------------------------------------------- F G M

Man returns back

C M ------------------------------------------------------------------------------------- F G

Takes chicken with him
        -------------------------------------------------------------------------------------- C M F G

River Crossing Puzzle

This puzzles is asked by interviewers to check the thinking of the candidates.

A man has to cross a river with a Fox, Chicken and grain. There is a boat available at the bank of the river to help him out. Since boat cannot handle much load the man can carry only one item at a time along with him.

He cannot leave fox and chicken together as Fox will eat the chicken. He cannot leave Chicken and grain together as Chicken will eat the grain.

Fox is not interested in grain so he can leave them together. How can the farmer get everything across the river.

Click here for the Solution

Three Color Marbles Puzzle Solution

Well the solution is simple. Most of the people get this puzzles in the first attempt without any hint.

You need to pick at least 4 marbles from the jar in worst case scenario to make sure that you get two marbles of the same color.

In the worst case scenario you may get three different color marbles in the first three attempts. But at the fourth attempt you will get any one of the three colors and hence you will get a pair of the same color marble.

Three Colour Marbles Puzzle

This Puzzle is sometimes asked in interview questions just to check how the person thinks.

You are given 1 jar which contains three different color marbles. The color of the marbles are Red,Green and Blue.

How many minimum marbles you have to pick from the jar to make sure that you get a pair of marbles of the same color.

Click here for the Solution

Race Puzzle Solution

Tom will lose again. This time Jerry started the race 10 meters behind the starting line so at 90 meter mark both will be at the same place in the race. Since Jerry is faster than Tom so he will cover the remaining 10 meter distance in less time compared to Tom. So Jerry will win the race again.

Race Puzzle

Tom and Jerry are in a 100 meter race. When Jerry crossed the finished line tom was at 90 meters mark. Jerry asked Tom to run one more race.

In the New race Jerry would start 10 meters behind the second line. All other things are same.

Will Tom win this time? or Will Jerry win the race again? or whether it will be a tie?

Click here for the Solution

Pill Puzzle Solution

Well there are lot of approaches to solve this puzzle. I will mention few of them.

1. Take one more pill from Bottle X. Now you have 4 pills in your hand. Now cut each of these pill into half and make sure to keep both the half at separate places. Now take the first half and you will be sure to get one pill X and one pill Y and take the other half tomorrow.

2. Take one more pill from bottle X and crush all the four pills to make a powder. Mix the powder well. Take half of the powder and keep half of the powder for your next use.

Pill Puzzle

A Patient has fallen ill and has been advised by doctor to take two pills daily. The two pills X and Y are indistinguishable and must be taken together.

The patient has to take two pills together otherwise the he will die. If he takes more than two pills at the same time he will die and if he takes one less pill or in different proportions he will die.

There are two bottles which contains these two pills. While taking out pills the person took one pill from Bottle X and accidentally he got two pills from Bottle Y. Now all the pills look the same.

The Pills are very costly and therefore the person does not want to waste it.How will he make sure that he eat just one pill of each type without wasting the pill?

Click here for the Solution

Fruit Jars Puzzle Solution

Well you need to pick just one fruit from the jar labelled as Apple and Oranges to correctly label the jars.

The trick here is to realize that all the jars are labelled incorrectly. So you will get the solution if you proceed thinking in this direction.

Let's take a scenario. Suppose you pick from jar labelled as Apple and Oranges and you got Apple from it. That means that jar should be Apple as it is incorrectly labelled. So it has to be Apple jar.
Now the jar labelled Oranges has to be Mixed as it cannot be the Oranges jar as they are wrongly labelled and the jar labelled Apple has to be Oranges.

Similar scenario applies if it's a Oranges taken out from the jar labelled as Apple and Oranges.

Fruit Jars Puzzle

This is the most commonly asked interview puzzle.

You have 3 jars that are all mislabeled. One jar contains Apple, another contains Oranges and the Third Jar contains a Mixture of both Apple and Oranges.

You are allowed to pick as many fruits as you want from each jar to fix the labels on the jars. What is the minimum number of fruits that you have to pick and from which jars to correctly label them?

Click here for the solution

Two Cubes Puzzle Solution

This puzzle is easy but you have to think out of the box to solve it.

We have two cubes so total 12 faces. So we can put 12 numbers on them. Since every month will have 11 and 22 so 1 and 2 should be kept on both the cubes. We have 10 number and 12 faces and we have to repeat two of them.

So it is simple. On 1st Cube:
The numbers will be 0,1,2,3,4,5
and on 2nd Cube we will have 1,2,6,7,8,9.

This looks fine but in the puzzle it is mentioned that the person uses both the cubes. So for date 4 it should be 04 but we cannot have it.So 0 should be kept on both the cubes. So then how we will arrange 13 numbers on 12 faces.

It's easy we can keep 6 on the cube and just turn it upside down to make it 9 whenever we want to use 9.
So the solution will be

1st Cube 0,1,2,3,4,5
2nd Cube 0,1,2,6,7,8

So you can make any combinations of dates using these cubes.

Two Cubes Puzzle

A person has two cubes at his home. Everyday he arranges both the cubes so that the front faces shows the current day of the month. What are the numbers present on both the Cubes so that the person can do this task?

Click here for the Solution

Cube Puzzle Solution

The pic itself will explain you the answer.

Give two cuts along the length, two cuts along the breadth and two cuts along the height.You will get 27 cubes of 1x1x1. So the minimum number of cuts required are Six.

Cube Puzzle

Well this is a simple Puzzle. You are given a 3x3x3 Cube.

You have to break it into 27 cubes of 1x1x1 each. How many minimum cuts you have to give to achieve this?

Note : A cut can go through Multiple Pieces.

Click here for the solution

Door Puzzle Solution

Well the solution to this puzzle is simple. Just think mathematically and you will get the answer.

Let's take the first scenario

You choose one of the door. So probability of getting the jackpot - 1/3.

Let's say that the jackpot is in Door no 1 and you choose Door no 1. So the angel will either open door no 2 or door no 3. Let's look at the sample space of this Puzzle.

                         Door1                                     Door2                             Door3
Case 1 :            Jackpot                                   Goat                                Goat
Case 2 :            Goat                                     Jackpot                              Goat
Case 3 :            Goat                                       Goat                              Jackpot

Now you have chosen to stick with door 1 so your chances of winning will be 1/3.
Now if you decide to change the door.
Let's say again you have chosen Door No 1 initially so the Angel will open Door 3 if it's the second case and if you switch you will win the jackpot. Similarly if it's Case 3 then Angel will open Door No 2 and if you switch you will win. So chances of winning the jackpot if you switch is 2/3.

Hence it is advisable to switch.

Door Puzzle

Well this is one of the most common puzzle asked in Interviews.

You are given a choice of three doors by an Angel. You can choose only one of the doors among the three. Out of these three doors two contains goat and one has a jackpot.

After you choose one of the doors she reveals one of the other two doors behind which there is a goat. Angel gives  you an opportunity to change the door or you can stick with your chosen door.

You don't know behind which door we have the goat.Should you switch or it doesn't matter?

Click here for the solution

50 Red and 50 Green Balls Puzzle Solution

Well the trick in the puzzle is that you have to maximize the probability of picking the Red ball. Now we know that the probability of picking one jar from two will be 1/2. So in order to increase the probability we need to do such that the whenever one jar is picked it gives only red balls and keeping the probability of picking the red ball in second jar also high.

Normal Scenario.
Let's say we do it like this
Jar A - 50 Red Balls
Jar B - 50 Green Balls

So Probability will be 0.5*1 + 0.5*0 = 0.5

But we are not getting any number from jar B as there is no Red Ball. So to increase the chances we do like this.

Jar A - 1 Red Ball
Jar B - 49 Red Balls and 50 Green Balls

So Probability will be 0.5*1 + 0.5 * (49/99) = 74/99.

So the maximum probability will be 74/99 of picking the red ball from a random jar.

50 Red and 50 Green Balls Puzzle

You are given two jars. You have 50 Red Balls and 50 Green Balls. You have to place all the balls in the jars such that when a random ball is picked from any random jar the chances of picking the Red ball is maximum. What will be the value of probability for the same.

Click here for the solution

Bee Puzzle Solution.

This puzzle is little confusing and on hearing for the first time people gets confused as to what is asked in the question.

Lets look at the puzzle.

Length of the tunnel = 200 km
Speed of train 1 = 100 km/h
Speed of train 2 = 100 km/h
Speed of Bee = 1000 km/h

So Relative velocity of both the trains as both are moving in opposite directions.
100+100 = 200 km/h.
So the time taken by the trains before the collision happened is 200/200 = 1 hour

So the bee will travel for 1 hour before the collision.
Speed of bee = 1000 km/h
so distance traveled by the bee will be 1000*1 = 1000 km before the collision would take place.
 

Bee Puzzle

This is one of the most commonly asked interview puzzle just to confuse the candidates.

Two trains enters a tunnel 200 km long traveling at 100 km/h from opposite ends.As soon as they enter the tunnel a fast flying bee with a speed of 1000 km/h starts from end of the tunnel and heads towards the other.As soon as the bee reached the other train it turns around and goes back to the first train and again turns around after reaching the first train. The two trains collide and the bee survived the collision. How much distance does the bee travels?

Click here for the solution

10 jars marbles Puzzle Solution

The trick in this puzzle is that you are allows to weigh just once and you have to figure out the jar which contains the defective marbles. The solution is simple.

Take 1 marble from jar 1,2 marbles from jar 2, 3 marbles from jar 3 ........ 10 marbles from jar 10. Now weigh these marbles on the weighing machine. Let's say the sum is
549 grams.

Now ideally the sum should be 550 grams(1*10 + 2*10 + 3*10 ................10*10) if all the marbles were of same weight. This means that one marble is defective.So this marble will be from jar 1 as we have taken just 1 marble from jar 1.So this means that jar 1 contains the marbles weighing 9 grams.

Similarly if the weight shown by the machine is 548 grams that means that the jar 2 contains the defective marbles and so on.

10 jars marbles puzzle

You are provided with 10 jars which contains marbles. One jar among the 10 contains marbles weighing 9 grams each whereas a regular marbles weighs 10 grams. You are provided with a weighing machine and you can just make a single weighing on the machine.There are infinite number of marbles in each jar. How will you decide which is the jar containing 9 grams marbles in just single weighing?

Click here for the solution

12 Ball Puzzle Solution

Well this is a enhancement to the already discussed 8 ball puzzle in puzzle arena. To start with remember that you can weigh maximum 3 times to arrive at the correct decision.

Divide the 12 balls into group of three. So we will have 4 balls in each group. Let's name the groups as A,B and C.
Now weigh any two groups one weighing balance. Let us take A and B for this scenario.
So there will be two possibilities.
1. Both A and B are equal.
2. One of them is Heavy.

Let's take the first case. If both are equal this means that the defective ball is in group  C. so take Group C and divide it into two groups of two balls each and weigh them. One of the group will weigh heavier. So for the third weighing weigh the two balls against each other and you can proceed.

Similarly for the second case.

You will know whether A is heavy or B is heavy. just proceed as done in case 1 and you will get the solution in 3 weighing.

12 Ball Puzzle

There are 12 black balls of equal size and shape.One of them is heavier than the other 11 balls. You are given a weighing balance.Now using not more than 3 weighing you have to find out which is the defective ball in the lot.

Click here for the Solution

17 horses puzzle solution

Well this puzzle is interesting. you have to think such that with the solution everybody is happy and no body has suffered a loss.

Let's see the problem first.
we have 17 horses to be divided among three sons with the ratio as given.

1st son -- half of the horses (17/2)=8.5
2nd son -- one third of horses (17/3)=5.66
3rd son -- one ninth of horses (17/9)=1.88

Now all the results are in fraction so the horses cannot be distributed like this. What will the traveling mathematician do to solve it.

It's simple.He will add his horse to the group of horses. So in total we have 18 horses now. Now let's see the scenario again.

1st son -- half of the horses (18/2)=9
2nd son -- one third of horses (18/3)=6
3rd son -- one ninth of horses (18/9)=2

So in total 17 horses will get distributed among the three sons and the traveling mathematician will take his horse and leave.

17 Horses Puzzle

A man wants to divide his 17 horses among his three sons. According to his will the oldest man should get half of the horses,the middle son should get one third of the horses and the youngest son should get one ninth of the horses.
When there father dies they were not able to divide the horses as the result was coming in fractions. As the sons were fighting on how to divide the horses a traveling mathematician came and heard their problem. He proposed a solution with which all the sons got their share in the property without harming any animal.
What was the advice given and how the group of houses were divided?

Click here for the solution.

How Investment Banker Thinks?

Found this interesting story told at a multinational investment banking firm. So thought of sharing it.

A manager at Goldman Sachs has this to tell.

Once upon a time in a village, a man announced to the villagers that he would buy monkeys for Rs 10. The villagers, seeing that there were many monkeys around, went out to the forest and started catching them.

The man bought thousands at Rs 10 and as supply started to diminish, the villagers stopped their effort.

He further announced that he would now buy at Rs 20. This renewed the efforts of the villagers and they started catching monkeys again.

Soon the supply diminished even further and people started going back to their farms. The offer rate increased to Rs 25 and the supply of monkeys became so little that it was an effort to even see a monkey, let alone catch it!

The man now announced that he would buy monkeys at Rs 50!

However, since he had to go to the city on some business, his assistant would now buy on behalf of him.

In the absence of the man, the assistant told the villagers, "Look at all these monkeys in the big cage that the man has collected. I will sell them to you at Rs 35 and when the man returns from the city, you can sell it to him for Rs 50."

The villagers squeezed up with all their savings and bought all the monkeys.

Then they never saw the man nor his assistant, only monkeys everywhere!

Welcome to 'Goldman Sachs'!!