What work can one never finish?

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.

What runs around the whole yard without moving?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

Can you count the number of triangles in the given figure?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

Solve this tricky question. You are trapped in a forest. With you, you have a gun preloaded with two bullets in it. In front of you, there is a tiger, a leopard and a jaguar.

How do you survive?

What does an Island and the letter T have in common?

What goes through cities and fields, but never moves?