AoPS Academy
. Prove that:
be reals such that 
Prove that 
Let be reals such that 
Prove that 
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 
, but how do we arrive at this using the I-E-P?
: 
is midpoint of 
is midpoint of 
is height. Prove that lines 
and 
intersect at one point.
, where 
is one base, meaning that 
lies on other line of base 
can't be base, because 
then means that - parallelogram and 
. Contradiction.
and 
.
instead of the correct 
, (indeed it is an isosceles trapezoid)
.
- centroid of 
.
.
to 
.