Problem #PRU-100447

Problems Algebra Number theory. Divisibility Division with remainders. Arithmetic of remainders Odd and even numbers

Problem

One sunny day Alice met the White Rabbit. The Rabbit told her that he owns a pocket watch which has 11 gears arranged in a chain loop. The rabbit asked Alice if it was possible for all the gears to rotate simultaneously. What is your opinion on this matter? Can all the gears rotate simultaneously?