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.

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

What four weights can be used to balance from 1 to 30 pounds?

You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.

Can you tell the eye color of the cab driver?

What two things can you never eat for breakfast?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

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