Day Before Tips
by elasticwealth, Mar 19, 2025, 12:09 AM
This post has been edited 2 times. Last edited by elasticwealth, Today at 4:15 AM
AMC 12 Question
by sadas123, Mar 18, 2025, 5:11 PM
This post has been edited 2 times. Last edited by sadas123, Yesterday at 5:15 PM
Tennessee Math Tournament (TMT) Online 2025
by TennesseeMathTournament, Mar 9, 2025, 7:30 PM
Attachments:
This post has been edited 2 times. Last edited by TennesseeMathTournament, Mar 16, 2025, 2:15 PM
10B Score Thread
by BS2012, Nov 13, 2024, 5:17 PM
EDIT: I found out i didn't silly #19, so i got 144
This post has been edited 2 times. Last edited by BS2012, Nov 13, 2024, 7:35 PM
Evan's mean blackboard game
by hwl0304, Apr 18, 2019, 10:58 PM
Two rational numbers 
and 
are written on a blackboard, where 
and 
are relatively prime positive integers. At any point, Evan may pick two of the numbers 
and 
written on the board and write either their arithmetic mean 
or their harmonic mean 
on the board as well. Find all pairs 
such that Evan can write 1 on the board in finitely many steps.
Proposed by Yannick Yao
and 
are written on a blackboard, where 
and 
are relatively prime positive integers. At any point, Evan may pick two of the numbers 
and 
written on the board and write either their arithmetic mean 
or their harmonic mean 
on the board as well. Find all pairs 
such that Evan can write 1 on the board in finitely many steps.Proposed by Yannick Yao
This post has been edited 1 time. Last edited by djmathman, Apr 19, 2019, 2:31 PM
Convolution of order f(n)
by trumpeter, Apr 17, 2019, 11:04 PM
Let 
be the set of positive integers. A function 
satisfies the equation ![\[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]](//latex.artofproblemsolving.com/2/e/7/2e73ff2f75b103e9d6a4004a42e4ed7f4ee64a67.png)
for all positive integers 
. Given this information, determine all possible values of 
.
Proposed by Evan Chen
be the set of positive integers. A function 
satisfies the equation ![\[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]](http://latex.artofproblemsolving.com/2/e/7/2e73ff2f75b103e9d6a4004a42e4ed7f4ee64a67.png)
for all positive integers 
. Given this information, determine all possible values of 
.Proposed by Evan Chen
This post has been edited 1 time. Last edited by trumpeter, Apr 17, 2019, 11:36 PM
Prove Collinearity
by tc1729, Apr 25, 2012, 9:55 PM
Let 
be a point in the plane of 
, and 
a line passing through . Let 
be the points where the reflections of lines 
with respect to intersect lines 
respectively. Prove that are collinear.
be a point in the plane of 
, and 
a line passing through . Let 
be the points where the reflections of lines 
with respect to intersect lines 
respectively. Prove that are collinear.This post has been edited 1 time. Last edited by tc1729, Apr 25, 2012, 9:56 PM
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