What has to be broken before you can use it?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

John and Jill are madly in love with each other. To remind Jill of his pure love, John wants to send her a ring by post but in their country where burglary is quite prominent, any package that is not locked comes under the risk of being stolen for the contents.

John and Jill possess many padlocks but neither one of them has the other key.

Can you find a way John can send the ring to Jill safely?

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 need to arrange three 7 and mathematical symbols to form number 1?

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

What brings you down but never up?

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

You are provided with a grid (as shown in the picture). Can you fill the squares with numbers 1-8 in a manner that none of the two consecutive numbers are placed next to each other in any direction (vertically, horizontally or diagonally?)

A girl rode into a tourist spot out of the city on Thursday. She loved the place and decided to stay for a few days. She stayed for four days and then she left for back home on Thursday.

How can this be possible?