If you’ve got me, you want to share me; if you share me, you haven’t kept me. 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.

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

Which digit occurred maximum times between the number 1 and 1000?

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

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?

On my way to St. Ives I saw a man with 7 wives. Each wife had 7 sacks. Each sack had 7 cats. Each cat had 7 kittens. Kittens, cats, sacks, wives. How many were going to St. Ives?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

John was piloting a plane behind a car but was never able to overtake it. Why?