   Chapter 9.4, Problem 5ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# (a) Given any set of four integers, must there be two that have the same remainder when divided by 3? Why? (b)Given any set of three integers, must there be two that have the same remainder when divided by 3? Why?

To determine

(a)

To check:

Whether there must be two that have the same remainder when divided by 3, if there is any set of four integers.

Explanation

Given information:

There is any set of four integers.

Concept used:

The pigeonhole principle states that if n+1 objects (e.g. pigeons) are to be distributed in n holes then some hole must contain at least two objects (pigeons).

Calculation:

Suppose there are the pigeon holes 3n+0,  3n+1,  3n+2 where n represents an integer

To determine

(b)

To check:

Whether there must be two that have the same remainder when divided by 3, if there is any set of three integers.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 