[/quote]
,
MathJuice bottles and Bob starts with 
MathJuice bottles. An unfair coin is then flipped, with probability 
of landing heads. If the coin lands heads, Alice gives Bob a bottle; otherwise, Bob gives Alice a bottle. This process repeats until someone runs out of bottles.
are such that 
,
of prime positive integers 
such that number 
equals to a square of an integer.
be real number greater than 
.![\[S=\log_a {bc}+\log_b {ca}+\log_c {ab}\]](http://latex.artofproblemsolving.com/5/9/e/59e1a33017116963165f744b49b8515f126c64ef.png)
.
for which:
for all 
.
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 
Y by
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So, there is a very important decision.. and I have decided to asked all of the people on AoPS 
I am going to MathCounts nats, but there is the MathCon a day before the competition. It there anything I will miss by just going to MathCounts right on the day of the contest, or is it worth it to go to MathCon, even if I will have to leave before the awards.
Just want your ideas and opinions for this
also pls say if there is something that I will miss in MathCounts before the actual contest
I am going to MathCounts nats, but there is the MathCon a day before the competition. It there anything I will miss by just going to MathCounts right on the day of the contest, or is it worth it to go to MathCon, even if I will have to leave before the awards.
Just want your ideas and opinions for this
also pls say if there is something that I will miss in MathCounts before the actual contest
