be a fixed integer. There are 
beads on a circular necklace. You wish to paint the beads using 
colors, such that among any 
consecutive beads every color appears at least once. Find the largest value of 
for which this task is 
possible.
This easy via the binomial theorem for the quantity is just 
,
and 
.
Y by Adventure10, Mango247
In a triangle 
, let 
and 
be the midpoints of 
and 
respectively. The distance from the midpoint of 
to the midpoint of 
is 
. What is the length of side 
?
, let 
and 
be the midpoints of 
and 
respectively. The distance from the midpoint of 
to the midpoint of 
is 
. What is the length of side 
?This post has been edited 1 time. Last edited by Leicich, Sep 1, 2014, 3:00 AM
,
.
and 
.
and 
,
.
.
and 
with common ratio 
,
the midpoint of 
and 
the midpoint of 
, we have that 
and in the same way 
, hence 
, so 
