Our product and our sum always give the same answer. Who are we?

Here is a conversation between a couple who both are software professionals.

Husband: Hey! What is your date of birth?
Wife Replied Angrily: It is 591062400
Husband after doing some calculations replied, "Got It".

What is the DOB of the wife?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

An evil man kidnapped someone and made them take one of two pills. One was harmless, but the other was poisonous. Whichever pill the victim took, the kidnapper took the other one. The victim took their pill with water and died. The kidnapper survived. How did the kidnapper get the harmless pill?

Can you solve below mathematical equation?

2^1234 - 2^1233

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

John is on an island and there are three crates of fruit that have washed up in front of him. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

Each crate is labelled. One reads 'apples', one reads 'oranges', and one reads 'apples and oranges'. He know that NONE of the crates have been labeled correctly - they are all wrong.

If he can only take out and look at just one of the pieces of fruit from just one of the crates, how can he label all of the crates correctly?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------