,![\[
1^2 + 2^2 + 3^2 + \ldots + k^2 = \frac{k(k + 1)(2k + 1)}{6}
\]](http://latex.artofproblemsolving.com/b/5/d/b5d49e25bd8d8a211b72372ff967558e1a8365ce.png)
Find the smallest positive integer 
is divisible by 200.
for real numbers 
.
of the triangle 
is extended beyond 
to 
so that 
.
is extended beyond 
to 
so that 
.
,
Y by
Ruby writes the numbers 
on the whiteboard. In each move, she selects two distinct numbers, 
and 
, erases them, and replaces them with 
. She repeats this process until only one number, 
, remains. What are all the possible values of ?
on the whiteboard. In each move, she selects two distinct numbers, 
and 
, erases them, and replaces them with 
. She repeats this process until only one number, 
, remains. What are all the possible values of ?
,
as well. This value is equal to 
,
.
.
