Who is in the barber shop?

Here is the problem:

One day, I was walking on the way to the barber shop. There are three barbers A, B and C, but they don't always stay in the barber shop. In addition, barber A is a famously known coward. A never leaves the barber shop without B. I saw from a distance that the barber shop was still open, indicating that there was at least one barber in it. I like the craft of barber C best, so I hope that C is in the barber's shop at this time.

According to the known conditions and current observations, I am very satisfied to conclude that C must be in the barber shop. My reasoning process is like this: to prove the contrary, suppose C is not in the barber shop. In this case, if A is not in the barber shop, then B must be in the shop, because there is at least one person in the shop; However, if A is not in the barber shop, B should not be in the barber shop, because A will not leave the barber shop without B. Therefore, from "C is not in the barber shop", two contradictory conclusions "if A is not in, B must be in" and "if A is not in, B must not be in".

This shows that the assumption that "C is not in the barber shop" is wrong.

Is my reasoning correct? If not, what is the problem?

• Please provide the name of the book Commented Jul 14, 2022 at 13:44
• Hum it's a book written in chinese; i am not sure it has a English translation, but I will put the name here for reference. ( 浴缸里的惊叹：256 道让你恍然大悟的趣题 -- by 顾森) Commented Jul 14, 2022 at 13:56