Story of 7 Generous Dwarfs

The Seven Dwarfs are having breakfast, and Snow White has just poured them some milk. Before drinking, the dwarfs have a ritual. First, Dwarf #1 splits his milk equally among his brothers' mugs (leaving himself with nothing). Then Dwarf #2 does the same with his milk, etc. The process continues around the table, until Dwarf #7 has distributed his milk in this way. (Note that Dwarf #7 is named Dopey!) At the end, each dwarf has exactly the same amount of milk as he started with!

 

How much milk does each cup contain, if there were 42 ounces of milk altogether?

Finding difficult? Click here for answer! 

Behind the Story of 7 Generous Dwarfs

What was the story?

First thing is very clear that Dwarf 7 must have 0 ounces of milk at the start and end. Let's assume that 'a' be the maximum amount of milk (in ounces) that any dwarf has in his mug at any point of time. 

For a moment, let's assume Dwarf 1 himself has this 'a' amount of milk.

Now, when D1 distributes his 'a' amount of milk among 6 others, D7 receives 'a/6' amount of milk. At this point of time somebody else will be having maximum amount of milk 'a'. Let D2 be that person now having milk 'a'.

Next is D2's turn where he gives a/6 to all. So now D1 has a/6, D7 has 2a/6 and somebody else say D3 has maximum a. Continuing in this way, for each Dwarf's turn gives - 

Now, when we assumed D2 has maximum milk amount a after receiving a/6 from D1, then it's clear that he must had earlier 5a/6. Similarly, D3 had maximum amount of milk a after receiving a/6 from D1 and D2 indicates that he had 4a/6 milk initially. Continuing in this way, we can find the amount of milk each had initially like below.

So at any point of time, the milk distribution is like a, 5a/6, 4a/6, 3a/6, 2a/6, a/6, 0 where amounts are distributed among 7 dwarfs in cyclic order. But the total amount of milk available is 42 ounces.Hence, 

a + 5a/6 + 4a/6 + 3a/6 + 2a/6 + a/6 +  0 = 42

a + 15a/6 = 42

a + 5a/2 = 42

7a = 84

a = 12.

That means at any point of time the maximum amount of milk that one dwarf can have is equal to 12 ounces. And then others would have 10, 8, 6, 4, 2, 0.

To conclude, the 7 dwarfs had 12, 10, 8, 6, 4, 2, 0 ounces of milk initially.  

"Who is The Killer?"

An eighty-year-old person was living alone in his house. On a sunny Friday morning, while delivering some letters in the mailbox, the postman felt suspicious and decided to look through the window of the house. That’s when he saw the old man lying dead on the floor in a puddle of blood. When the police arrived, they found three bottles of milk, the Tuesday’s newspaper, and some gifts in front of the house. The lock of the door was broken, and they already suspected a person.

Whom and why?

He might be the murderer! 

Little Mistake By The Murderer!

What was the incident?

The police suspected the newspaper straightaway.

Since there were 3 bottles of milk, it's clear that the old man died 3 days ago i.e. on Tuesday & milkman didn't have idea of it. Hence, he has dropped milk bottles there. 

But the newspaper boy knew that the old man is no more in this world hence he didn't drop newspaper since Wednesday. 

  

Would You Help This Farmer ?

A farmer had 25 cows. To identify easily he numbered them from 1 to 25. Interestingly, each cow produces liters of milk equal to the respective number given. For example, a cow numbered 5 gives 5 liters of milk or a cow numbered 18 produces 18 liters of milk. Now that farmer had 5 sons. Farmer wants to share those 25 cows among his 5 sons with each son getting 5 cows. But he wants to make sure each son would get equal amount of milk.

How should he make 5 groups of cows to distribute among his sons?

Please, Help me!

This is what farmer need to do! 

Fair Distribution of Farmer's Cows

What was the interesting?

First let's name 5 sons as A,B,C,D & E. Now look at the image below.

Just collect numbers surrounded by same shapes. If you observe carefully answer, a difference of 4 created at one place which is compensated at other 4. Each son would be getting 65 liters of milk.

Fair Distribution of Cows