Difference between revisions of "2006 SMT/General Problems/Problem 16"
(Created page with "==Solution== The condition we are looking for is <math>35(n-1)\equiv 0 \mod 360</math>, because if any other <math>A_n = A_1</math> than <math>35(n-1)</math> must be a multip...") |
m (→Solution) |
||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | Points <math> A_1, A_2, \cdots </math> are placed on a circle with center <math> O </math> such that <math> \angle OA_nA_{n+1}=35^\circ </math> and <math> A_n\not=A_{n+2} </math> for all positive integers <math> n </math>. What is the smallest <math> n>1 </math> for which <math> A_n=A_1 </math>? | ||
| + | |||
| + | |||
==Solution== | ==Solution== | ||
Revision as of 17:35, 14 January 2020
Problem
Points 
are placed on a circle with center 
such that 
and 
for all positive integers 
. What is the smallest 
for which 
?
Solution
The condition we are looking for is 
, because if any other 
than 
must be a multiple of 360 as we have rotated 
by the time we place 
.
![\[35(n-1)\equiv 0\mod 360 \Rightarrow 5(n-1)\equiv 0\mod 360 \Rightarrow x\equiv 73,1\mod 360\]](http://latex.artofproblemsolving.com/5/1/6/51672d662853f1f28fa3a76b19dfde031b1e2d09.png)
We can ignore the case of 
because be are looking for an 
. Therefore, our answer is the second lowest option, 
or 
