No one wants to have it, but if one got it, he does not want to lose it. What is It?

Mr. Buttons was all set to go to the village of Buttonland to meet his friend. So, he packed his bags and left for the village at 5 in the morning. Upon travelling on a road for miles, he came across a point where the road diverged into two. He was confused on which road to take. He gazed around and he saw two owls sitting on a branch. He thought he could ask for directions for the village from the two owls. So he went to the tree. There he saw a sign which read, "One owl always lies, and one is always truthful. They both fly away if you ask them more than 1 question."
Mr. Buttons was caught in the dilemma of what to ask? And from which owl to ask, since he only had one question. What should Mr. Buttons ask?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

If,

A = 1

B = 2

C = 3

...

...

Z = 26.

Based on above rule, you need to find an eleven letter word whose letter sum is equal to 52.

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

what does the below math rebus puzzle mean?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?