   Chapter 9.4, Problem 35ES ### 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
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# Given a set of 52 distinct integers, show that there must be 2 whose sum or defference is diveisibele by 100.

To determine

To show that there must be 2 integers whose sum or difference is divisible by 100.

Explanation

Given:

Given a set of 52 distinct integers.

Calculation:

Let us suppose there are boxes labeled as 0,199,298,.....,50.

According to the pigeonhole principle if N+1 letters were to be placed in N   pigeonholes, then at least one of these pigeonholes must receive more than one letter.

So there must be chosen 51=(521) pigeonholes and place the 52 integers in these pigeonholes in such a way that either sum or difference of two numbers should be divisible by 100

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