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Showing posts from November, 2017

### The Coconut Problem

Ten people land on a deserted island. There they find lots of coconuts and a monkeys. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night one castaway wakes up hungry and decides to take his share early. After dividing up the coconuts he finds he is one coconut short of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey's coconut to have a total evenly divisible by 10. However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up hungry and decides to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to 1/9 of the total pile. After dividing them up into nine piles he is again one coconut short and tries to take the monkey's slightly bloodied coconut. The monkey conks the second man on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the 10th person to wake up gets the entire pile for himself. What is the smallest number of possible coconuts in the pile, not counting the monkeys?

### Number Of Coconuts In The Pile

Absolutely no need to overthink on the extra details given there. Just for a moment, we assume the number of coconuts in the community pile is divisible by 10,9,8,7,6,5,4,3,2,1.

Such a number in mathematics is called as LCM. And LCM in this case is 2520. Since each time 1 coconut was falling short of equal distribution there must be 2519 coconut in the pile initially. Let's verify the fact for all 10 distributions tried by 10 people.Each time monkey kills 1 person & number of persons among which coconuts to be distributed decreases by 1 each time.

### Wise Men In Survival Game

A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads.

Once lined up, they must not communicate among themselves. Nor may they attempt to look behind them or remove their own hat.The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.

The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.The king will then move on to the next wise man and repeat the question.

The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.

What is the maximum number of men they can be guaranteed to save?

### Master Plan By Wise Men

Why this master plan needed?

99 can be guaranteed to save! How?

Even if the person behind calls out the color of the hat that next person is wearing both would be survived only if they are wearing same color of hat.

So how 99 can be saved?

For a simplicity, let's assume there are only 10 wise men & (only) assume we are among them. Now, we need to make a master plan to survive from this game of death.

One of us need to agree to sacrifice his life to save 9 of us & this person would be the first one in line. He will be survived of he has good luck.

The first person in line should shout RED if he founds number of RED hats even otherwise he should shout BLUE. Now if he has good luck then the hat color of his own hat would match & he would be survived.

The clue given by the first person is very important. Right from second person everyone need to count number of RED hats in front of him. Additionally, the next person need to keep track of number of RED hats that people behind him are wearing.

### The Greek Philosophers

One day three Greek philosophers settled under the shade of an olive tree, opened a bottle of Retsina, and began a lengthy discussion of the Fundamental Ontological Question: Why does anything exist?

After a while, they began to ramble. Then, one by one, they fell asleep.

While the men slept, three owls, one above each philosopher, completed their digestive process, dropped a present on each philosopher's forehead, the flew off with a noisy "hoot." Perhaps the hoot awakened the philosophers.

As soon as they looked at each other, all three began, simultaneously, to laugh.

Then, one of them abruptly stopped laughing. Why?

### Theory Of The Smartest Philosopher

The one who stopped laughing was the smartest one among! Read how he was the smartest.

We need to think from the smartest Philosopher's point of view. Let's name 2 other Philosophers as A & B.

Now here is what the smartest Philosopher would think.

"If I had nothing on my head then A & B must have been laughing after looking each other's head. And at least one of them is smart enough to realize that the other is laughing only after looking at him. That means A (or B) would have realized that the some thing is on his head too as B (or A) is laughing after looking him (not me if I had nothing on my head). Hence one of them would have stopped laughing. Since they are not stopping to laugh, I too must have something on my head."

Hence the smartest Philosopher stopped laughing after realizing that the fact.

A brilliant puzzle based on the similar logic is here!

### Logic Problem: The Trainee Technician

A 120 wire cable has been laid firmly underground between two telephone exchanges located 10km apart.Unfortunately after the cable was laid it was discovered to be the wrong type, the problem is the individual wires are not labeled. There is no visual way of knowing which wire is which and thus connections at either end is not immediately possible.

You are a trainee technician and your boss has asked you to identify and label the wires at both ends without ripping it all up. You have no transport and only a battery and light bulb to test continuity. You do have tape and pen for labeling the wires.

What is the shortest distance in kilometers you will need to walk to correctly identify and label each wire?

### To Be A Skilled Technician

The shortest distance is 20 km! Surprised? Read further.

Let's name the two exchanges as a 1 & 2 respectively. Now at end 1, let's make a groups of wires having 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 number of wires. Now somebody might ask why not 15 groups having 8 wires in each. After reading the entire process here, we'll get the answer of it.So we 15 groups have total 1 + 2 + 3....+ 15 = 120 wires. Let's name these groups as A, B, C, D ...... O. That means group A has 1, B has 2, C has 3 wires & so on.

Now join together all the wires of the particular group. For example, 2 wires of group B should be joined together, 7 wires of G tied together & so on. The sole wire of A is left as it is.

We will take the battery & bulb to other end traveling 10 km. We will say a wire is paired with the other if the bulb gets illuminated if battery & bulb connected in between.

Now let's take any wire at the other end & find the number of wires that are pairing with that particular wire under test. We will group such wires & label with those exactly how we labeled at end 1.

For example, if we find 2 wires pairing with particular wire then that wire & 2 paired wires together to be grouped in 3 wires & labeled as C.The sole wire not getting paired with any will be labeled as A. And group with wire pairing with 7 other wires together should be labeled as H.

In this way, we will have the exact group structure that we have at end 1. By now, we have identified & labeled correctly wires in groups of 1,2,3,....15 wires at both ends.

Now, we are going to label each wire of group by it's group & count number. For example, the only wire in group A labeled as A1, 2 wires in B are labeled as B1,B2, wires in G are labeled as G1,G2,G3,G4,G5,G6,G7 and so on.

Now, at end 2 itself, what we are going to do is connecting first wire of each group to A1. Second wire of each group to be connected to B2, third of each to be connected to C3 and so on. (refer the diagram above, where labels of wires that are to be connected together are written in same color).

### Magical Water Well & Pilgrim

In a small town, there are three temples in a row and a well in front of each temple. A pilgrim came to the town with certain number of flowers.

Before entering the first temple, he washed all the flowers he had with the water of well. To his surprise, flowers doubled. He offered few flowers to the God in the first temple and moved to the second temple. Here also, before entering the temple he washed the remaining flowers with the water of well. And again his flowers doubled. He offered few flowers to the God in second temple and moved to the third temple. Here also, his flowers doubled after washing them with water. He offered few flowers to the God in third temple.

There were no flowers left when pilgrim came out of third temple and he offered same number of flowers to the God in all three temples. What is the minimum number of flowers the pilgrim had initially? How many flower did he offer to each God?

Source

### Flowers Owned By Pilgrim

Let's assume that the pilgrim had X number of flowers initially. Suppose that he offered Y flowers to the each God.

Before entering into the first temple, magical well doubled the flowers he had initially. That means he had 2X flowers before entering into first temple. After offering Y flowers, he had 2X - Y flowers.

Again after visiting first temple he washed flowers in magical well where number of flowers gets doubled. Now, he had 4X - 2Y.

Out of these 4X - 2Y, he offered Y flowers to God in second temple. So he had 4X - 2Y - Y = 4X - 3Y flowers after visiting second temple.

These 4X - 3Y doubled to 8X - 6Y after washing in magical water well.

At third temple, he offered all the flowers he had which in turn equal to Y as we assumed.

8X - 6Y = Y

8X = 7Y

X/Y = 7/8

This is the ratio of the flowers that pilgrim had to the flowers he offered to each God.

In general, the pilgrim had 7N flowers initially and he offered 8N flowers to each God, where N = 1, 2, 3, 4,

Let's cross verify same with N = 1, meaning that the pilgrim had 7 flowers initially & offered 8 flowers to each God.

Before entering into first temple, the flowers doubled to 14. Out of which, 8 offered at first temple & left 6.

Again 6 doubled to 12 at magical well & 8 out of 12 offered to God at second temple leaving behind 4.

Those 4 again doubled to 8 by magical well & all 8 offered to God at third temple.

### Time Taken For The Journey

A RED ant is sitting on one side of a table (point X) and a BLACK ant is sitting on the opposite side of the table (point Y).

Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the RED ant to move to point Y and it takes 5 seconds for the BLACK ant to reach point X.

Find out the total time taken by the RED and the BLACK ant to make the journey.

### Calculation of Time For The Journey

What was the journey?

Let the speed of RED ant is R & that of BLACK ant is B

Let time taken by them to meet be T.

Now we will apply the basic formula of distance:

Distance = Speed * Time.

The
RED ant travels R T distance before meeting and 20 R after the meeting.

The
BLACK ant travels B T distance before meeting and 5 B after the meeting.

Now as per the question,The distance traveled by RED ant before they both meet will be equal to the distance covered by BLACK ant after they meet. We can say the same for the vice versa case as well.

Thus,

RT = 5B and BT = 20R
i.e. B = 20R/T, putting in RT = 5B

R T = [20R/T] * 5

RT = 100R/T

T^2 = 100

T = 10.

Thus the RED ant will require 10 + 20 = 30 seconds to travel the distance.

And the
BLACK ant will take 10 + 5 = 15 seconds to travel the distance.

### Flip The Triangle

Here you see a triangle formed by ten coins. The triangle points upwards. How can just three coins be moved to make the triangle point downwards?

 Flip It By Moving 3

### Flipped The Triangle!

Here should be those 3 coins that you need to move so that the triangle point towards down.

And after moving those coin, it will look like,

### Distance Between Houses?

Four friends built a colony for themselves. They built their own houses at different
distances from each other.

Chris lived 60 km away from Alex.
Darren lived 40 km away from Bill.
Chris lived 10 km nearer to Darren than he lived to Bill.

Can you find out how far was Darren's house from Alex?

### Locations of 4 Friends

Let's represent houses of friends by their initial letter of the name i.e. C is the house of Chris, D is the house of Darren, B is Bill's house & A is name of Alex's house.

Now C & A are located at 60 km away from each other while D & B are 40 km apart i.e. CA = 60 & DB = 40.

As per given data, D is 10 km nearer than B from C. Hence, CB = CD + 10

There are 5 possibilities of the locations of these 4 friends.

Case 1. D & B are in between C & A.

In this case,

CD + DB + BA = 60

but DB = 40,

CD + BA = 20,

CB - 10 + BA = 20

CB + BA = 30 i.e. CA = 30

But CA = 60, hence this combination is not possible. Other way, CB >= 40, since CD = CB-10, CD >= 30. That means CD + DB >= 70 for which B needs to be beyond A as CA = 60.

Case 2 : A is between D & B.

In this case, CD + DA  = 60, DA + AB = 40 . If we subtract second one from first, we get,

CD - AB = 20

CB - 10 - AB = 20

CB - AB = 30

CA = 30 but CA = 60. Hence, this combination too is invalid.

### This Coffee Puzzle Harder Than You Think!

With all credits to the creator of this picture puzzle, here it is just reproduced once again.

So what do you think, which coffee cup will fill up first?

Hint : Don't conclude early!

 Coffee Cup Puzzle

This should be the first one!

### Only This Cup Will Fill Up!

Purpose of the title of the post!

If you think that cup 4 will fill up first then you are deceived by the creator successfully.  You might have found the order of filling cups as 4,9,7 & 5. Congrats, your brain hasn't processed details! Didn't you notice the blocks?

 Coffee Cup Puzzle

### Finding The Average Speed

A man drives his car to the office at 20miles/hr. After reaching the office, he realizes that it's a new year holiday so he went back home at a speed of 30miles/hr.

Discounting the time spent in the stoppage what was his average speed of his journey?

### Right Way To Find The Average Speed

What was the given data?

If you are finding average speed of 2 given speeds as (Speed 1 + Speed 2)/2 then you are getting tricked by questioner. The speed itself is a distance covered per unit i.e. Speed = Distance/Time. Calculating average speed like that means,you are doing like,

Average Speed = (Speed1 + Speed2)/2

= (Distance1/Time1 + Distance 2/Time2)/2

So you need to find the total distance traveled & the total time taken to complete the entire journey.It should be like,

Average Speed = Total Distance/Total Time

= (Distance1 + Distance2)/(Time1 + Time2)

In the given problem, let D be the distance traveled by car to the office. Let T1 be the time required to go to the office & T2 be the time to return back.

Since, Speed = Distance / Time, Time = Distance / Speed.

Hence,

T1 = D / 20

T2 = D / 30

Now,

Total distance traveled =  D + D = 2D, Total Time taken = T1 + T2

Hence,

Average Speed = 2D / (T1 + T2)

Average Speed = 2D / (D/20 + D/30)

Average Speed = 2D / (50D/600)

Average Speed = 2D / (D / 12)

Average Speed = 24 miles/hr.

Therefore, the average speed of the journey is 24 miles/hr not 25 miles/hr [(20 + 30)/2].

### Guess The Order Of Cards

A man sitting opposite you has four cards in his hand facing him: 2, 3, 4 and 5 (but not in that order). He wants them placed in ascending order from his left to his right. To do this, he takes the leftmost card (from your perspective) and puts it last. He then takes the third card from the right (your right) and puts it in the last place.

What was the previous order of the cards?

 Order Of Cards?

### Identified The Order of The Cards

Since he puts the leftmost card (from our point of view) to it's opposite location that card must be 2 (that's the smallest one & needs to be first in ascending order).

So the last card (from his point of view) must be 2. We still don't know exact positions of 3,4,5. Now 2 is in first position

Now what he does is that, moves third card from his left (our right) to the last position. Now to be in ascending order the last card must be 5. So the card that he used in this move must be 5.

Since these 2 moves completes the ascending order, rest must be in ascending from left to right already i.e as 3 & 4 but 5 in between them.

Hence the order before he moved cards must be as 3,5,4,2.

 Previous Order of The Cards

### Time Of Arrival?

One day Rohit decided to walk all the way from city Bangalore to Tumkur. He started exactly at noon. And Samit in city Tumkur decided to walk all the way to Bangalore from Tumkur and he started exactly at 2 P.M. on the same day.

Both met on the Bangalore - Tumkur Road at five past four, and both reached their corresponding destination at exactly the same time.

At what time did we both arrive?

 Beginning of Journey

### Finding The Time Of Arrival

Let 'x' km/minute be the speed of Rohit's walk. He started to walk at 12 PM & met Samit at 4:05 PM. That means he has walked for 245 minutes.

Distance traveled by Rohit = 245x km

Let 'y' km/minute be the speed of Samit's walk. He started to walk at 2 PM & met Samit at 4:05 PM. That means he has walked for 125 minutes.

Distance traveled by Samit = 125y km

 Time of Meeting

Now after meeting each other they resumed their journey further. That means Rohit continues to Tumkur & covers distance of 125y km at his speed of x km/minute. Time taken by him further to complete the journey is 125y / x minutes (Time = Distance/Speed).

### Journey From Top To Ground

Galileo dropped balls of various weights from the top of the Leaning Tower of Pisa to refute an Aristotelian belief that heavier objects fall faster than lighter objects.

If the balls were dropped from a height of 54 meters, how long did it take for the balls to hit the ground?

### Time Needed To Reach The Ground

To solve the problem, we need to remember what we have learned in our early days of school. The gravity of the earth accelerates the falling object at the rate of 9.8 meter per second square. We know, the kinematic equation,

s = ut + (1/2) a t^2   .......(1)

where,

s = distance covered,
u = initial velocity,
a = acceleration,
t = time taken to travel distance s.

In this case, initial velocity must be 0 as it is dropped from height 54m. Again height here is the distance covered by the object. And the acceleration in this case is nothing but the acceleration due to gravity which is 9.8 m/s^2.

So putting s = 54 m, u = 0 m/s, a = 9.8 m/s^2 in equation (1) above,

54 = 0 x t + (1/2) x 9.8 x t^2

54 = 4.9 t^2

t^2 = 11.021

t = 3.3 seconds.

So theoretically both balls should take 3.3 seconds to reach the ground. But resistance due to air will make the difference in time taken by balls to hit the ground.

### Round Table Coin Game

You are sitting with one opponent at an empty, round table. Taking turns, you should place one dollar on the table, in such a way that it touches none of the coins that are already on the table. The first player that is not able to place a dollar on the table has lost. By tossing a coin, it has been decided that you may start.

Which strategy will you follow to make sure you are guaranteed to win?

### Never Loose Round Table Coin Game

There is little trick with which you will always end on winning side in this Round Table Coin Game. Since you have got first chance to place the coin you should place the coin right at the center of the round table. Now for every next coin placed by opponent you need to place coin in such a way that it 'mirrors' opponent's coin.

Imagine line from the center to opponent's coin. Place your coin exactly opposite to that coin at distance equal to distance between center & opponent's coin. Or imagine a circle (with the center fixed at the round table) with opponent's coin lying on it's border.  And place your coin at diagonally opposite point of point where opponent placed coin on that imaginary circle. (Assume imaginary circle though it's not appearing perfectly in the image above)

In this way for every move of your opponent, you will have 'answer' in form of space for placing the coin. This will continue until last place left on the table with your turn of placing the coin in the end.

This is how to make sure you always on winning side in this 'Round Table Coin Game'!