# Find the missing room

13 people came into a hotel with 12 rooms and each guest wanted his own room. The bellboy solved this problem. He asked the thirteenth guest to wait a little with the first guest in room number 1. So in the first room there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the twelfth guest to room number 11. Then he returned to room number 1 and took the thirteenth guest to room number 12, still vacant. How can everybody have his own room?

• What happened to Guest 2? Jun 16, 2016 at 8:03
• Waiting for room... Jun 16, 2016 at 8:30

There is a flaw in the system:

Second guest in not accommodated in any of the room.

That's why it may appear that all guests fit with their own room.

Following statement is used to confuse the listerner

[...] He asked the thirteenth guest to wait a little with the first guest in room number 1. So in the first room there were two people. The bellboy took the third guest to room number 2 [...]

The bellboy...

Was one of the 13 people. Only 12 of them were guests.

• The problem says "thirteenth guest", which implies at least 13 guests existing there (or fourteen, if you index from zero!) Jun 16, 2016 at 11:01

The flaw is that:

There are still two guests in room 2.

The puzzle says:

The bellboy took the third guest to room number 2

but

room number 2 is already occupied by a guest. The bellboy does nothing to resolve this double occupation.