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...") |
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+ | ==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>? | ||
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==Solution== | ==Solution== | ||
Revision as of 18:35, 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
.
We can ignore the case of because be are looking for an
. Therefore, our answer is the second lowest option,
or