Difference between revisions of "1993 AHSME Problems/Problem 30"

(Created page with "== Problem == Given <math>0\le x_0<1</math>, let <cmath> x_n=\left\{ \begin{tabular}{ll} 2x_{n-1} &\text{ if }2x_{n-1}<1 \\ 2x_{n-1}-1 &\text{ if }2x_{n-1}\ge 1 \end{tabular}} <...")
 
m (Problem)
Line 2: Line 2:
 
Given <math>0\le x_0<1</math>, let  
 
Given <math>0\le x_0<1</math>, let  
 
<cmath>
 
<cmath>
x_n=\left\{ \begin{tabular}{ll}
+
x_n=\left\{ \begin{array}{ll}
 
2x_{n-1} &\text{ if }2x_{n-1}<1 \\
 
2x_{n-1} &\text{ if }2x_{n-1}<1 \\
 
2x_{n-1}-1 &\text{ if }2x_{n-1}\ge 1
 
2x_{n-1}-1 &\text{ if }2x_{n-1}\ge 1
\end{tabular}}
+
\end{array}\right.
 
</cmath>
 
</cmath>
 
for all integers <math>n>0</math>. For how many <math>x_0</math> is it true that <math>x_0=x_5</math>?
 
for all integers <math>n>0</math>. For how many <math>x_0</math> is it true that <math>x_0=x_5</math>?

Revision as of 20:09, 10 March 2015

Problem

Given $0\le x_0<1$, let \[x_n=\left\{ \begin{array}{ll} 2x_{n-1} &\text{ if }2x_{n-1}<1 \\ 2x_{n-1}-1 &\text{ if }2x_{n-1}\ge 1 \end{array}\right.\] for all integers $n>0$. For how many $x_0$ is it true that $x_0=x_5$?

$\text{(A) 0} \quad \text{(B) 1} \quad \text{(C) 5} \quad \text{(D) 31} \quad \text{(E) }\infty$

Solution

$\fbox{D}$

See also

1993 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 29
Followed by
Problem 30
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All AHSME Problems and Solutions

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