What is the centre of gravity?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

What is the unique property of the following words ?
* Revive
* Banana
* Grammar
* Voodoo
* Assess
* Potato
* Dresser
* Uneven

Can you replace the question mark with the correct number in the below table sequence?

What has a ring but no finger?

What's the only room from which no one can enter or leave

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

You want to boil a two-minute egg. If you only have a three-minute timer (hourglass), a four-minute timer and a five-minute timer, how can you boil the egg for only two minutes?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?