Will the Sheep Survive?

Hundred tigers and one sheep are put on a magic island that only has grass. Tigers can live on grass, but they want to eat sheep. If a Tiger bites the Sheep then it will become a sheep itself. If 2 tigers attack a sheep, only the first tiger to bite converts into a sheep. Tigers don’t mind being a sheep, but they have a risk of getting eaten by another tiger.

All tigers are intelligent and want to survive. 

Will the sheep survive?

Survival chances of the sheep are - Click Here! 

Survival Chances of the Sheep

Why sheep is in danger?

First let's see what happens when there are different number of tigers present on 
the island. Remember we are talking about survival of the sheep that is initially present n the island and not sheep converted from tiger.

1. Suppose there are only 1 tiger and 1 sheep on the island. Then, the tiger will eat 
    the sheep and won't have fear of being eaten up after transformation into sheep 
    as there is not tiger left. 

    The sheep will not survive.

2. Let's suppose there are 2 tigers and 1 sheep present. Each intelligent tiger can think - 

    ----------------------------------------------------------------------------------------------------------
   "If I eat a sheep then I will be converted into sheep and other tiger would eat me
    as it would result into '1 tiger and 1 sheep' scenario above in (1). 

    So, I should not take risk"
    ---------------------------------------------------------------------------------------------------------- 

    The sheep will be survived.


3. Now suppose there are 3 tigers and 1 sheep are on the island. Each tiger would think-  
     ----------------------------------------------------------------------------------------------------------
    "If I target the sheep and get converted into sheep itself then on the island there
     would be 2 tigers and 1 sheep as above case (2). 

     As per that, none of other 2 tiger would dare to attack me and I would be 
     survived as a sheep in the end. 

     So better I should attack the sheep and anyhow I will be survived in the end as a
     sheep"
     ----------------------------------------------------------------------------------------------------------
      The sheep will not survive.

4. Finally, suppose there are 4 tigers and 1 sheep. Now, each tiger can put logic like -       ----------------------------------------------------------------------------------------------------------
    "If I attack the only sheep and get myself converted to sheep then this case 
     will be reduced to '3 tigers and 1 sheep' as in case (3). 

     In that case, the sheep has 0 chance of survival in the end. 

     That means, my life will be in danger as in above case (3), if I attack 
     this sheep toget converted into sheep. Better, I shouldn't attack"
     ----------------------------------------------------------------------------------------------------------
     The sheep will be survived.

Conclusion : 

If observed carefully, it can be concluded that the sheep will be survived when there are EVEN number of tigers (Case 2 and Case 4) are present. And obviously, will be in danger when there are ODD number of tigers present on the island.

In the given situation, there are 100 tigers on the island which is EVEN number. That means, as per above conclusion the only sheep on the island will be survived.

 

Truth Tellers and Liars in Circle

On a certain island there live only knights, who always tell the truth, and knaves, who always lie.

One day you find 10 island natives standing in a circle. Each one states: "Both people next to me are knaves!"

Of the 10 in the circle, what is the minimum possible number of knights?

Do you think there can be 5?

Identifying Number of Truth Tellers in Circle

What was the task given?

Recalling the given situation. 

On a certain island there live only knights, who always tell the truth, and knaves, who always lie.

One day you find 10 island natives standing in a circle. Each one states: "Both people next to me are knaves!"

 
Every Knight must be surrounded by 2 Knaves and every Knave has to be surrounded by at least one knight to satisfy the given condition. So there must be Knave-Knight-Knave groups must be standing in circle. 

Now if Knave of previous group is counted for the next group, then there will be 5 knights in the circle as shown below.

But the question asks minimum possible number of Knights in the circle.

So after forming 3 groups of Knave-Knight-Knave separately (total 9 in circle), the last person will be obviously surrounded by 2 knaves. Hence, he must be Knight. See below.

This way there can be only 4 knights standing in the circle without violating the given condition.
 

The Green-Eyed Logic Puzzle

In the green-eyed logic puzzle, there is an island of 100 perfectly logical prisoners who have green eyes—but they don't know that. They have been trapped on the island since birth, have never seen a mirror, and have never discussed their eye color.

On the island, green-eyed people are allowed to leave, but only if they go alone, at night, to a guard booth, where the guard will examine eye color and either let the person go (green eyes) or throw them in the volcano (non-green eyes). The people don't know their own eye color; they can never discuss or learn their own eye color; they can only leave at night; and they are given only a single hint when someone from the outside visits the island. That's a tough life!

One day, a visitor comes to the island. The visitor tells the prisoners: "At least one of you has green eyes." 

On the 100th morning after, all the prisoners are gone, all having asked to leave on the night before. 

How did they figure it out?


Here is the solution! 

The Green-Eyed Puzzle Solution

Here is that Puzzle! 

Nobody is going to dare to go the guard unless he is absolutely sure that he is green eyed; otherwise it would be suicidal move.

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For a moment, let's assume there are only 2 prisoners named A & B trapped on island.

On first day, A is watching green eyed B & B can see green-eyed A. But both are not sure what is color of their own eyes. Instead, A(or B) waited B(or A) to escape from island since he is green-eyed. Rather both are sure that other too doesn't know anything about color of own eyes.

On next morning both see each other still on island. Here is what A thinks.

If I was non green-eyed then B would have realized that the person pointed by visitor in his statement ('at least one of you have green eyes') is himself. Hence, B would have realized that he is green-eyed & could have escaped easily. Since B didn't try to escape that means I too must have green eyes.

So A can conclude that he too have green eyes. Exactly same way, B concludes that he too has green eyes. Hence, on next day both can escape from the island.
 
Note that, if the night of the day on which visitor made statement is counted then next day would have 1st morning & 2nd night since visitor's visit. Now since A & B left on 2nd night, we can't see anybody on 2nd morning next day.

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Now let's assume there are 3 prisoners named A,B and C trapped on island.

Let's think from A's point of view as an example.What he thinks.

Let me assume I don't have green eyes.Now each B and C could see 1 green-eyed & other non green-eyed person. But still they don't know color of own eyes.So on that night nobody tries to escape.

On first morning I see both B and C still present there.

Now B can think that if he has no green eyes then C could have concluded that the person pointed by visitor's statement ('at least one of you have green eyes') is C himself (as both A & B are non green-eyed. This way, C would have realized that he is green-eyed.

In a very similar way, B would have realized that he too is green-eyed.

Now both of them could have escaped on that night as they are sure that they are green-eyed.

But on the second morning, I see again both of them are still there. So now I can conclude that I too have green eyes.

If A can conclude then why can't B and C?  So after seeing each other on 3rd day, each of 3 can conclude color of eyes is green. Now on 3rd night they all can escape safely.

This is called as inductive logic.

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If observed carefully, 2 prisoners need 2 nights and 3 prisoners need 3 nights to logically deduce that the each of them is green-eyed.

Hence, 100 prisoners would require 100 nights to absolutely make sure that each of them is green eyed.

That's why on the 100th morning day, there is no prisoner present on island. 

An Island Of Puzzles

There is an Island of puzzles where numbers 1 - 9 want to cross the river.

There is a single boat that can take numbers from one side to the other.

However, maximum 3 numbers can go at a time and of course, the boat cannot sail on its own so one number must come back after reaching to another side.

Also, the sum of numbers crossing at a time must be a square number.

You need to plan trips such that minimum trips are needed.

This should be that minimum number! 

Numbers On An Island Of Puzzles

What was the challenge?

We need only 7 trips to send all digits across the river.

1. Send 2, 5, 9 (sum is 16).

2. Bring back the 9.

3. Send 3,4, 9 (sum is 16).

4. Bring back the 9.

5. Now send 1,7,8 (sum is 16).

6. Bring back the 1.

7. And finally send 1,6,9 (sum is 16).

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?

Here is that smallest number! 

Source 

Number Of Coconuts In The Pile

What was the problem? 

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.

How To Reach The Island?

Abhijeet wants to reach an island which is in the middle of the river. The island is 30 feet from the edge of the river. As shown in the picture below he got two wooden planks about 29 feet each.

          How to reach there?

How can Abhijeet reach the island? 

1. This is how he reached!

Source 
 

Trick To Reach The Island.

Here is the task! 

A picture is worth thousands of words.

  Finally, reached there!