[/quote]
,
for which:
for all 
.
,
,
and point 
lies inside triangle 
.
and 
meet 
and 
,
intersects 
and 
at points 
and 
,
is cyclic if and only if 
bisects 
.
such that 
,
,
are all equal to
,
be real numbers, such that 
.
.
,
(where 
are the digits and 
)
For example the permutation sum of 20253 is 
Let 
and 
be two fivedigit integers with the same permutation sum.
.
be the incircle of triangle 
.
is parallel to side 
and tangent to 
is parallel to side 
and tangent to 
and incenter 
.
meets 
at 
and meets 
;
cuts 
.
and 
,
is the midpoint of 
.
and 
intersect at points 
and 
.
or 
.
be non-negative real numbers such that 
.![\[a\sqrt{1+b^{3}}+b\sqrt{1+c^{3}}+c\sqrt{1+a^{3}}\le 5.\]](http://latex.artofproblemsolving.com/f/f/a/ffaeec844a6bdf10a96e8e9d298ef97ac839d713.png)
,
,
,
satisfying: ![\[a_{k+1}=\frac{a_k^2+1}{a_{k-1}+1}-1\]](http://latex.artofproblemsolving.com/7/b/4/7b4ab849cdc409906514e2ebb688802f17df41ea.png)
for every 
with 
.
Y by adarshnet, ahaanomegas, mathway, yrushi, 171282, Adventure10, and 13 other users
PM AIME15/Binomial-Theorem to add your marathon/make any changes to this list
The following list will include Archived Tournaments, Inactive Problem a day Marathons, Active Tournaments, and "running" marathons.
Definition of Archived Tournaments-Tournaments that have a defined end, and have reached that ending spot are defined as archived tournaments.
Definition of Active Problem a day Marathons - The game moderator of the tournament has not set a defined deadline, however, the tournament is dead, and has the results (from the last post of the tournament creator’s scores)
Definition of Inactive Tournament- The game moderator is inactive or few users still compete in the tournament. “Problems of the day” marathons that ended will be included in this list.
Definition of Running Marathons- A marathon where a user asks a question and posts a new question. To be included in this list, the tournament must be mathematical (word marathon, long word marathon, you name it, etc. are not counted), and it must be active (last post in under a month ago and the thread must be on the first page of the forum it is in).
The following list will include Archived Tournaments, Inactive Problem a day Marathons, Active Tournaments, and "running" marathons.
Definition of Archived Tournaments-Tournaments that have a defined end, and have reached that ending spot are defined as archived tournaments.
Definition of Active Problem a day Marathons - The game moderator of the tournament has not set a defined deadline, however, the tournament is dead, and has the results (from the last post of the tournament creator’s scores)
Definition of Inactive Tournament- The game moderator is inactive or few users still compete in the tournament. “Problems of the day” marathons that ended will be included in this list.
Definition of Running Marathons- A marathon where a user asks a question and posts a new question. To be included in this list, the tournament must be mathematical (word marathon, long word marathon, you name it, etc. are not counted), and it must be active (last post in under a month ago and the thread must be on the first page of the forum it is in).
This post has been edited 40 times. Last edited by Binomial-theorem, Jul 27, 2011, 7:03 AM
You may search for inactive marathons, too. There are so many such marathons on fora.
