Problem - 02 - National Math Camp 2021 Combinatorics Test - "The result is invariant"
Posted: Fri Apr 30, 2021 5:22 pm
There are $2021$ stones in a pile. At each step, Lazim chooses a pile with at least two stones, splits it into two piles, and multiplies the sizes of the resulting two piles. He keeps doing this until there are $2021$ piles each containing exactly one stone. Finally, he adds up all the products he obtains during the process and ends up with the number $N$. Find, with proof, all the possible values of $N$.