I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

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?

I can be cracked, made, told, and played. What am I?

There is a jar in which there are two types of candies.
20 blueberries and 16 strawberries. You perform the following steps:
1) You take out two candies.
2) If the two candies are of the same flavour, you add a blueberry one otherwise, you add the strawberry one.

You repeat these two steps till there is just one candy remaining in the jar. Which flavoured candy will be left?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

How many times in a given day, minutes and hour clock comes in a straight line ?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

If you drop a 15 kg iron bar and a 5 kg bag of cotton from a height of 50 meters which will reach the ground first?

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