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

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

What is wrong in the below Picture?

Can you make the number 24 by utilizing the numbers 1, 3, 4 and 6? You must use one number only one time and you can use mathematical operation symbols anytime anywhere.

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

How many times do a clock's hands overlap in a day ?

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

What is the largest number you can write with just 3 digits?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?