I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

A river should be crossed by a father, a mother and their two sons and two daughters.
There are some rules that should be followed while crossing the river. There can be only two people in the raft while crossing. The daughters cannot be with their father unless there is the presence of the mother. The sons cannot be with their mothers unless the father is present. Unless the guard is on the board, the criminals cannot be with any of the family members. Only the adults like the father, the guard, and the mother knows to use the raft.

How will they cross the river?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where's the father?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?