[/quote]
,
such that for any two infinite sequences of positive integers 
and 
,
for all 
,
such that 
for all 
.
and 
be two isogonal conjugate with respect to triangle 
.
and 
be two points lying on the circle 
such that 
and 
are perpendicular and parallel to bisector of 
,
and 
bisect two arcs 
containing 
and not containing 
.
such that there exists an integer 
satisfying
,
)
denote the set of positive integers
such that for all 
it holds that 
such that 
.
such that
for all 
.
be a positive integer. Megavan and Minivan are playing a game, where Megavan secretly chooses a real number 
in ![$[0, 1]$](http://latex.artofproblemsolving.com/a/b/1/ab178d831a786b92cb4c9ddc2d33578223036f98.png)
.
and submits to Megavan, where Megavan replies immediately with one of 
,
,
,
The answers in the form of 
if the answer is in the form 
if in the form 
and every 
.
such that 
and 
.
be the minimum number of queries that Minivan needs in order to guarantee success, regardless of Megavan's strategy. Prove that 
with the set 
such that each element in the permutations has at most one immediate neighbor greater than itself.
with 
and 
.
on 
is 
.
is 
.
is parallel to 
.
Y by
Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! 
Please hide solutions and answers, hints are fine though!
The first problem is:
Please hide solutions and answers, hints are fine though!
The first problem is:
March 21st Problem wrote:
Alice flips a fair coin until she gets 2 heads in a row, or a tail and then a head. What is the probability that she stopped after 2 heads in a row? Express your answer as a common fraction.
This post has been edited 1 time. Last edited by Leeoz, Friday at 10:02 PM
