Why is a river so rich ?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

What word is represented by this rebus?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

A man desired to get into his work building, however he had forgotten his code.
However, he did recollect five pieces of information
* Fifth number + Third number = 14
* The fourth number is one more than the second number.
* The first number is one less than twice the second number.
* The second number and the third number equals 10.
* The sum of all five numbers is 30.

What is the code ?

The King of a distant land had heard that Birbal was one of the wisest men in the East and so desired to meet Birbal. He sent Birbal an invitation to visit his country.

In due course, Birbal arrived in the distant kingdom. When he entered the palace he was flabbergasted to find not one but six kings seated there. All looked alike. All were dressed in kingly robes. Who was the real king?

The very next moment he got his answer. Confidently, he approached the king and bowed to him.

How did Birbal know who was the real king?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?