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}} <...") |
Mathgeek2006 (talk | contribs) 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{ | + | 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{ | + | \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 19:09, 10 March 2015
Problem
Given 
, let
![\[x_n=\left\{ \begin{array}{ll} 2x_{n-1} &\text{ if }2x_{n-1}<1 \\ 2x_{n-1}-1 &\text{ if }2x_{n-1}\ge 1 \end{array}\right.\]](http://latex.artofproblemsolving.com/a/d/d/add03b886de5d53f623800ed6d402891d52ff5c6.png)
for all integers 
. For how many 
is it true that 
?
Solution
See also
| 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. 
