9. An inventory consists of a list of 115 items, each marked "available" or “unavailable." There are 60 available items. Show that there are at least two available items in the list exactly four items apart. (Hint: use the Pigeonhole principle)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 37E: Prove or disprove that AB=AC implies B=C.
icon
Related questions
icon
Concept explainers
Topic Video
Question
9.
An inventory consists of a list of 115 items, each marked
"available" or “unavailable." There are 60 available items. Show that
there are at least two available items in the list exactly four items apart.
(Hint: use the Pigeonhole principle)
Transcribed Image Text:9. An inventory consists of a list of 115 items, each marked "available" or “unavailable." There are 60 available items. Show that there are at least two available items in the list exactly four items apart. (Hint: use the Pigeonhole principle)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,