How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

4 fathers, 2 grand-fathers and 4 sons went to watch the movie.What is the minimum number of tickets they need to buy ?

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

Take away the whole and some still remain. What is it?

Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left hand? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.) If you cannot estimate the number then try to guess how long the number would be.