Task 101
Task 101: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. A $100$-gon $P 1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $100$ vertices equals 2009. The midpoints of the sides of $P 1$ form a second $100$-gon, $P 2$. Finally, the…
The task
A $100$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $100$ vertices equals 2009. The midpoints of the sides of $P_1$ form a second $100$-gon, $P_2$. Finally, the midpoints of the sides of $P_2$ form a third $100$-gon, $P_3$. Find the sum of the $x$-coordinates of the vertices of $P_3$.