1993 AHSME Problems/Problem 30

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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. ! Missing $ inserted.)

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
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
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