6. (a) Show, using the pigeonhole principle, that in any set of 5 integers, at least two have the same remainder when divided by 4. (b) Use the extended pigeonhole principle to show that there are at least 3 ways of choosing 2 different numbers from 2, 3, 4, 5, 6, 7,8,9 so that all choices have the same sum.
6. (a) Show, using the pigeonhole principle, that in any set of 5 integers, at least two have the same remainder when divided by 4. (b) Use the extended pigeonhole principle to show that there are at least 3 ways of choosing 2 different numbers from 2, 3, 4, 5, 6, 7,8,9 so that all choices have the same sum.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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