A plane crashed between the border of Mexico and America. Where do you bury the survivors?

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 am a prime number.
The double of myself is equal to the square of me.

which number am I?

I don't get anymore wetter, no matter how much rain falls on me.

Take 9 from 6, 10 from 9, 50 from 40, and leave 6.

How Come ??

What came first, the chicken or the egg?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

Five thieves looted a bank and they ran away in a car. The bank staff informed the police and they began the search of their car in their jeep. They found them on a road and chased them eventually catching them. The light that is used to fill the number plate was broken on the thieves' car. Also, the headlights of the jeep police were not working. How were the police able to catch the thieves then?