exercise:1aedb9c792: Difference between revisions

Latest revision as of 17:02, 14 June 2024

In a popular computer game the computer picks an integerfrom 1 to [math]n[/math] at random. The player is given [math]k[/math] chances to guess the number. After each guess the computer responds “correct,” “too small,” or “too big.”

Show that if [math]n \leq 2^k - 1[/math], then there is a strategy that guarantees you will correctly guess the number in [math]k[/math] tries.
Show that if [math]n \geq 2^k - 1[/math], there is a strategy that assures you of identifying one of [math]2^k - 1[/math] numbers and hence gives a probability of [math](2^k - 1)/n[/math] of winning. Why is this an optimal strategy? Illustrate your result in terms of the case [math]n = 9[/math] and [math]k = 3[/math].

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+In a popular computer game the computer picks an integerfrom 1 to <math>n</math> at random.  The player is given <math>k</math> chances to guess the number.  After each guess the computer responds “correct,” “too small,” or “too big.”
-\newcommand{\NA}{{\rm NA}}
+<ul style="list-style-type:lower-alpha"><li> Show that if <math>n \leq 2^k - 1</math>, then there is a strategy that guarantees you
-\newcommand{\mat}[1]{{\bf#1}}
-\newcommand{\exref}[1]{\ref{##1}}
-\newcommand{\secstoprocess}{\all}
-\newcommand{\NA}{{\rm NA}}
-\newcommand{\mathds}{\mathbb}</math></div> In a popular computer game the computer picks an integer
-from 1 to <math>n</math> at random.  The player is given <math>k</math> chances to guess the number.  After
-each guess the computer responds “correct,” “too small,” or “too big.”
-<ul><li> Show that if <math>n \leq 2^k - 1</math>, then there is a strategy that guarantees you
 will correctly guess the number in <math>k</math> tries.
 </li>