# Suppose that Hilbert’s Grand Hotel is fully occupied, but

## Problem 6E Chapter 2.5

Discrete Mathematics and Its Applications | 7th Edition

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Problem 6E

Suppose that Hilbert’s Grand Hotel is fully occupied, but the hotel closes all the even numbered rooms for maintenance. Show that all guests can remain in the hotel.

Step-by-Step Solution:

Step 1 :

In this problem in the Hilbert’s Grand Hotel is fully occupied, but the hotel closes all the even numbered rooms for maintenance then we have to prove that all guests can remain in the hotel.

Given in the problem by closing even numbered rooms,

Then we have the rooms number {1,3,5……}

All available room numbers are in the form of ,

Step 2 :

It is possible to move all the guest in even and odd room numbers to odd room numbers where k is an odd numbers are free.

.’. Guests in even numbered rooms  move to .

Guests in odd numbered rooms move to

Step 3 of 3

##### ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 6E from chapter: 2.5 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “Suppose that Hilbert’s Grand Hotel is fully occupied, but the hotel closes all the even numbered rooms for maintenance. Show that all guests can remain in the hotel.” is broken down into a number of easy to follow steps, and 28 words. This full solution covers the following key subjects: Hotel, maintenance, fully, grand, guests. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. Since the solution to 6E from 2.5 chapter was answered, more than 440 students have viewed the full step-by-step answer.

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