Question

(5 points) Monotonically Decreasing Function: Adversary Argument You are playing adversary to a player who is trying to guess when does a monotonically decreasing real-valued function defined on positive integers (that you have in mind) becomes negative for the first time. Your goal is to force the player to ask as many questions as possible. Recall that a monotonically decreasing function $f(n)$ satisfies the following property: $f(i) < f(j)$ for $i > j$. The player begins by asking the first question: What is the value of $f(1)$? You, the adversary responds, 256. [Oops, did you make a mistake? You don't have to answer this question.] Assuming that the player plans to ask the values of $f(2)$, $f(2^2)$, ..., $f(2^n)$, (a) What is the number of questions you can force the player to ask before a correct answer can be produced? [$f(1)$ is the first question, $f(2)$ is 2 questions, and so on...] (b) Write down the exact answers (or a strategy) that you will use to answer the player's questions.

          (5 points) Monotonically Decreasing Function: Adversary Argument
You are playing adversary to a player who is trying to guess when does
a monotonically decreasing real-valued function defined on positive integers (that you have in mind) becomes negative for the first time.
Your goal is to force the player to ask as many questions as possible.
Recall that a monotonically decreasing function $f(n)$ satisfies the following property: $f(i) < f(j)$ for $i > j$.
The player begins by asking the first question: What is the value of $f(1)$?
You, the adversary responds, 256. [Oops, did you make a mistake? You
don't have to answer this question.]
Assuming that the player plans to ask the values of $f(2)$, $f(2^2)$, ..., $f(2^n)$,
(a) What is the number of questions you can force the player to ask
before a correct answer can be produced? [$f(1)$ is the first question, $f(2)$ is 2 questions, and so on...]
(b) Write down the exact answers (or a strategy) that you will use to
answer the player's questions.

(5 points) Monotonically Decreasing Function: Adversary Argument
You are playing adversary to a player who is trying to guess when does
a monotonically decreasing real-valued function defined on positive integers (that you have in mind) becomes negative for the first time.
Your goal is to force the player to ask as many questions as possible.
Recall that a monotonically decreasing function f(n) satisfies the following property: f(i) < f(j) for i > j.
The player begins by asking the first question: What is the value of f(1)?
You, the adversary responds, 256. [Oops, did you make a mistake? You
don't have to answer this question.]
Assuming that the player plans to ask the values of f(2), f(2^2), ..., f(2^n),
(a) What is the number of questions you can force the player to ask
before a correct answer can be produced? [f(1) is the first question, f(2) is 2 questions, and so on...]
(b) Write down the exact answers (or a strategy) that you will use to
answer the player's questions.

Added by Samantha H.

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