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.

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

Can you find the dog hidden in a group of pandas?

I make a loud sound when I’m changing. When I do change, I get bigger but weigh less. What am I?

Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

What kind of band never plays music?