[/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
Just curious, what does everyone think about the prestige of a USAMO qualification vs a USAJMO qual? Obv USAMO > USAJMO but how much?
And while we’re at it, what about amc 10 dhr vs amc 12 dhr? Thoughts?
Edit: also how much is a perfect score on 10/12 worth? Asking for a friend….
And while we’re at it, what about amc 10 dhr vs amc 12 dhr? Thoughts?
Edit: also how much is a perfect score on 10/12 worth? Asking for a friend….
This post has been edited 1 time. Last edited by elasticwealth, Feb 17, 2025, 4:16 AM
)
