2023 AIME Proposals
by djmathman, Feb 19, 2023, 6:37 PM
for the last time?
AIME I #8 (January 2021). Rhombus
has 
. There is a point 
on the incircle of the rhombus such that the distances from to lines 
, 
, and 
are 
, 
, and 
, respectively. Find the perimeter of .
AIME II #5 (June 2020). Let
be the set of all positive rational numbers 
such that when the two numbers and 
are written as fractions in lowest terms, the sum of the numerator and denominator of one fraction is the same as the sum of the numerator and denominator of the other fraction. The sum of all the elements of can be expressed in the form 
, where 
and 
are relatively prime positive integers. Find 
.
AIME II #9 (April 2021). Circles
and 
intersect at two points and 
, and their common tangent line closer to intersects and at points 
and 
, respectively. The line parallel to line that passes through intersects and for the second time at points 
and 
, respectively. Suppose 
and 
. Then the area of trapezoid 
is 
where 
and 
are positive integers and is not divisible by the square of any prime. Find 
.
AIME II #10 (August 2020). Let
be the number of ways to place the integers 
through 
in the cells of a 
grid so that for any two cells sharing a side, the difference between the numbers in those cells is not divisible by 
. One way to do this is shown below. Find the number of positive integer divisors of .
![[asy] size(160); defaultpen(linewidth(0.6)); for(int j=0;j<=6;j=j+1) { draw((j,0)--(j,2)); } for(int i=0;i<=2;i=i+1) { draw((0,i)--(6,i)); } for(int k=1;k<=12;k=k+1) { label("$"+((string) k)+"$",(floor((k-1)/2)+0.5,k%2+0.5)); } [/asy]](//latex.artofproblemsolving.com/d/4/4/d44f3cfa87ba6099c5f197a4ada7a1e4da002e87.png)
Pretty happy with this set. Interestingly enough, my favorite problem is the combinatorics #10; this one was written only two weeks before 10A #14, so I might have been on a combi hot streak then.
I'm also pleasantly surprised people still like my geometry problems, despite the fact that the telltale signs of an altigeo are pretty obvious at this point. That might also be why I've stopped making them for now; they all kinda felt same-y to me and I haven't gotten the same joy out of them as I used to. (I did make one a few weeks ago, but other than that I haven't focused much on contest math.)
In any case, that'll be it for a while. As I mentioned before, I didn't submit anything for the 2023-2024 series of contests, so you probably won't see any dj problems there. I probably won't be completely dead, but I certainly don't feel the same passion and fire for problem construction as I used to. (Right now, I'm more focused on improving my mental well-being anyway.)
AIME I #8 (January 2021). Rhombus
has 
. There is a point 
on the incircle of the rhombus such that the distances from to lines 
, 
, and 
are 
, 
, and 
, respectively. Find the perimeter of .AIME II #5 (June 2020). Let
be the set of all positive rational numbers 
such that when the two numbers and 
are written as fractions in lowest terms, the sum of the numerator and denominator of one fraction is the same as the sum of the numerator and denominator of the other fraction. The sum of all the elements of can be expressed in the form 
, where 
and 
are relatively prime positive integers. Find 
.AIME II #9 (April 2021). Circles
and 
intersect at two points and 
, and their common tangent line closer to intersects and at points 
and 
, respectively. The line parallel to line that passes through intersects and for the second time at points 
and 
, respectively. Suppose 
and 
. Then the area of trapezoid 
is 
where 
and 
are positive integers and is not divisible by the square of any prime. Find 
.AIME II #10 (August 2020). Let
be the number of ways to place the integers 
through 
in the cells of a 
grid so that for any two cells sharing a side, the difference between the numbers in those cells is not divisible by 
. One way to do this is shown below. Find the number of positive integer divisors of .![[asy] size(160); defaultpen(linewidth(0.6)); for(int j=0;j<=6;j=j+1) { draw((j,0)--(j,2)); } for(int i=0;i<=2;i=i+1) { draw((0,i)--(6,i)); } for(int k=1;k<=12;k=k+1) { label("$"+((string) k)+"$",(floor((k-1)/2)+0.5,k%2+0.5)); } [/asy]](http://latex.artofproblemsolving.com/d/4/4/d44f3cfa87ba6099c5f197a4ada7a1e4da002e87.png)
Pretty happy with this set. Interestingly enough, my favorite problem is the combinatorics #10; this one was written only two weeks before 10A #14, so I might have been on a combi hot streak then.
I'm also pleasantly surprised people still like my geometry problems, despite the fact that the telltale signs of an altigeo are pretty obvious at this point. That might also be why I've stopped making them for now; they all kinda felt same-y to me and I haven't gotten the same joy out of them as I used to. (I did make one a few weeks ago, but other than that I haven't focused much on contest math.)
In any case, that'll be it for a while. As I mentioned before, I didn't submit anything for the 2023-2024 series of contests, so you probably won't see any dj problems there. I probably won't be completely dead, but I certainly don't feel the same passion and fire for problem construction as I used to. (Right now, I'm more focused on improving my mental well-being anyway.)
April 2025
November 2024