Can you find out the remainder when 3^300 is divided by 5?

Spot the cat in the picture below

You walk into a room and see a bed. On the bed, there are two dogs, five cats, a giraffe, six cows, and a goose. There are also three doves flying above the bed. How many legs are on the floor?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

A King wants to send the diamond ring to his girlfriend securely. He got multiple locks and their corresponding keys. His girlfriend does not have any keys to these locks and if he sends the key without a lock, the key can be copied in the way. How can King send the ring to his girlfriend securely?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

What number comes next in the series?

5 15 5 18 5 24 14 20 _

A father's child, a mother's child, yet no one's son.

Who am I?