vhylbyyy | | tt tt VAVAVAVA A MY YI | i tt tt tt tt tT
Traversing an Infinite Plane with a Line
The infinite hotel is full. A man comes to the front desk and asks for a room. The hotel manager says, “I’m terribly sorry, but we are full... But I may be able to help you. Let me think” He ponders for a moment and then says, “OK - I’ve found you a room? He calls the people in room 1 and asks them to move into room 2. He calls the people in room 2 and explains that due to a double booking they must move out of their room to let the people from room | in. But it’s OK; they can move into room 3. Everyone moves up a room and the new guest gets the checks into the now vacant room I.
This is a little harder to understand. We did not have a perfect one- to-one match as with the rooms and mini-bars. We had a mismatch of guests to rooms. But, we were able to show it is possible to re-establish a one-to-one match by doing something to every guest, having them move up a room. There is no problem with the last guest because it is an infinite hotel, there is no last guest! Another way to visualize the problem is to ask ever hunter to pass their spear to the right in the picture below.
HOUSE_OVERSIGHT_015873