I shave every day, but my beard stays the same. What am I?

Why 1729 is a magic number? Answer Logically.

What number do you get when you multiply all of the numbers on a telephone's number pad?

Can you place six X (crosses) in below board without making three in a row in any way ?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

Find the missing letter in the last circle logically in the given below picture.

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

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

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

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?