Question: Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. The gossip problem asks for G(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. a). Find G(1), G(2), G(3), and G(4). b). Use mathematical induction to prove that G(n)< 2n – 4 for n > 4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.] c). Prove that G(n)= 2n – 4 for n> 4.
Question: Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. The gossip problem asks for G(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. a). Find G(1), G(2), G(3), and G(4). b). Use mathematical induction to prove that G(n)< 2n – 4 for n > 4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.] c). Prove that G(n)= 2n – 4 for n> 4.
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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![Question: Suppose there are n people in a group, each aware
of a scandal no one else in the group knows about. These people
communicate by telephone; when two people in the group talk,
they share information about all scandals each knows about. For
example, on the first call, two people share information, so by
the end of the call, each of these people knows about two
scandals. The gossip problem asks for G(n), the minimum
number of telephone calls that are needed for all n people to
learn about all the scandals.
a). Find G(1), G(2), G(3), and G(4).
b). Use mathematical induction to prove that G(n)< 2n – 4 for n
> 4. [Hint: In the inductive step, have a new person call a
particular person at the start and at the end.]
c). Prove that G(n)= 2n – 4 for n> 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec115c85-217a-42e7-a90b-945bb14683b9%2Fade22fe1-433a-4a1c-8e4a-76c507db3a0b%2Fczkgcb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question: Suppose there are n people in a group, each aware
of a scandal no one else in the group knows about. These people
communicate by telephone; when two people in the group talk,
they share information about all scandals each knows about. For
example, on the first call, two people share information, so by
the end of the call, each of these people knows about two
scandals. The gossip problem asks for G(n), the minimum
number of telephone calls that are needed for all n people to
learn about all the scandals.
a). Find G(1), G(2), G(3), and G(4).
b). Use mathematical induction to prove that G(n)< 2n – 4 for n
> 4. [Hint: In the inductive step, have a new person call a
particular person at the start and at the end.]
c). Prove that G(n)= 2n – 4 for n> 4.
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