1993 AHSME Problems/Problem 30

Problem

Given $0\le x_0<1$ , let

\[x_n=\left\{ \begin{tabular}{ll}
2x_{n-1} &\text{ if }2x_{n-1}<1 \\
2x_{n-1}-1 &\text{ if }2x_{n-1}\ge 1
\end{tabular}}\] (Error compiling LaTeX. Unknown error_msg)

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

$\fbox{D}$

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 29	Followed by Problem 30
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1993 AHSME Problems/Problem 30

Problem

Solution

See also