Talk:2024 AIME I Problems/Problem 12

This problem's answer is wrong. When I completed this test, I did this problem wrong, too, because I missed this crucial (and weird) thing as mentioned below.

It is a very bad problem because there is actually another intersection if you look closely in Geogebra or other drawing tools. It is nearly impossible for humans to find.

Near the point (1, 1), not only is there an intersection at point (1, 1), but also another intersection at around (0.99, 0.99).

Here is the graph for proof:

RE: Bad graph

Note that although solution 1 is the first solution, it is not necessarily the intended one (which it probably isn't). I also acknowledged this in the note section, and should be hard to notice, as a hump and a non-zero sloped line that passes through its peak must also pass through another point of the hump.

Also this doesn't immediately mean that this is a bad problem.

Solution 1 seems a bit deceptive

How can one possibly count hundreds of intersections???

RE: Solution 1

Don't ask. I spend 20 minutes of my life drawing that graph during AIME and I am NOT doing it again