Question

Hilbert’s hotel has rooms numbered 1, 2, 3, 4, 5, . . . – one room for each positive integer. Guests are sometimes asked to move rooms, but never more than once a day. Guests are never asked to share a room with anyone else, and guests are never turned away. Guests often arrive to Hilbert’s hotel in one of his special buses. Each bus holds passengers numbered 1, 2, 3, 4, 5, . . . – one passenger for each positive integer. 1. Our story opens with Hilbert’s hotel empty. A bus full of guests arrive at Hilbert’s hotel. (a) How can Hilbert assign people to rooms?

Answer 1

For every even numbered room an even numbered guest is assigned to it and for every odd numbered room an odd numbered guest is assigned to it

Explanation:

Given that the Hotel is empty and every passenger stands for each positive integer and each number of room represents positive numbers as well

Hilbert can assign people to rooms by using a plot of first come first serve

i.e. For every even numbered room an even numbered guest is assigned to it and for every odd numbered room an odd numbered guest is assigned to it