[/quote]
,
sigmas = 
looksmaxxers, and 
looksmaxxers = 
skibdis, how many skibidis are in a sigma? Express your answer as a common fraction
be an equilateral triangle. Let 
be a point inside of it such that the square root of the distance of 
be a triangle. On side 
take points 
and 
such that 
take points 
and 
such that 
and on side 
take points 
such that 
Let 
and 
are concurrent.
lie the following points: 
and 
on 
,
on 
,
on 
.![\[
P = AM\cap BN,\quad
R = KM\cap LN,\quad
S = KN\cap LM,
\]](http://latex.artofproblemsolving.com/7/e/a/7ea90a0f1261ed7445bbac58fb0cdd76810259f3.png)
and let the line 
meet 
.
,
are collinear.
.
intersects 
and 
and 
,
of triangle 
lies on the circle 
and 
coincide.
be a triangle and 
and 
be two points on 
,
such that 
and let 
.
to the interior angle bisector of 
intersect 
in 
.
.
,
be its incenter. Incircle touches sides 
at 
,
to 
, respectively. Rays 
intersect 
at 
,
touches incircle at 
.
.
.
and 
are equal.
let 
and 
,
and 
.
and 
,
.
.
,
,
at points 
be the projection of 
.
intersects the circumcircle of 
.
and 
intersect 
and 
respectively. Prove that the lines 
,
,
are concurrent.
Y by
Hello, I was wondering if it's possible to make 8 with the numbers 5, 3, 5, and 7 under the following rules:
-You can only use 5 twice, 3 once, and 7 once.
-You must use all the numbers.
You can stack numbers to form larger numbers (example: I could take 3 and 5 and turn it into 35 or 53, or use 7, 3, and 5 to make 375.)
-You are allowed to use parentheses.
(Also, I already found out that no 3 digital numbers will work for the solution.)
-You can only use 5 twice, 3 once, and 7 once.
-You must use all the numbers.
You can stack numbers to form larger numbers (example: I could take 3 and 5 and turn it into 35 or 53, or use 7, 3, and 5 to make 375.)
-You are allowed to use parentheses.
(Also, I already found out that no 3 digital numbers will work for the solution.)
![\[|P\left(\left\lfloor \sqrt{\sqrt{\left\lceil \sqrt{\left\lfloor \sqrt{\left\lceil \sqrt{\sqrt{\left\lfloor \sqrt{\sqrt{\left\lceil \sqrt{\sqrt{\sqrt{5537}}}\right\rceil !!}}\right\rfloor !}}\right\rceil !}\right\rfloor !}\right\rceil !}}\right\rfloor\right)|\]](http://latex.artofproblemsolving.com/8/7/b/87ba34a74433ea04a72832926fdbc4a618408d4c.png)
![\[
(5 + 5) - (7 - 3) = 8
\]](http://latex.artofproblemsolving.com/e/c/5/ec56494a3dde4ad303e38f5d9e94cb84428e1a51.png)
.
.
.
,
where | | denotes cardinality
,
is equal to 8, so he solved the problem, he is not using eight
