Math Problem 1: Thirteen People in Twelve Rooms
A hotel manager had accidentally overbooked his hotel, and had to figure out how to fit thirteen people into only twelve rooms. After some careful thought, he discovered how to do it:
- He warned the thirteenth person in advance that he would have to be temporarily placed in the first room.
- He then placed the others, one per room, beginning with the first room.
- So, two people were in the first room, a third person was placed in the second room, a fourth person was placed in the third room, etc.
- Continuing to the end, the eleventh person was placed in the tenth room, and the twelfth person was placed in the eleventh room.
- This left the twelfth room free, so the hotel manager moved the thirteenth person (who was temporarily placed in the first room) into the twelfth room.
Problem solved! Thirteen people in twelve rooms, each with their own room!
Obviously, this is not possible. Where is the logical fallacy?
How many people actually arrived at the hotel?
Only twelve people arrived at the hotel. In step 1, we are told the thirteenth person would be temporarily placed in the first room, but that person is counted as the second person in step 3. The person called the "thirteenth" person in step 5 was actually the second person. The real thirteenth person never arrived.