There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

Once while in his court, King Akbar asked Birbal to write something on a wall that makes one sad when read in good times and makes one happy when read in sad times.

He took only a few moment and wrote something that fit the requirements. What did he write?

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?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

A quarter is one-fourth of a dollar but Mr. John has changed the equation as below :

DOLLAR * 4 = QUARTER

Can you replace each letter with a digit to make the above solution correct?

Make a sentence consisting of three words that have the whole alphabet.

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?