Problem - 02 - National Math Camp 2021 Combinatorics Test - "The result is invariant"
- Anindya Biswas
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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 $N$.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
— John von Neumann
— John von Neumann
- Mehrab4226
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Re: Problem - 02 - National Math Camp 2021 Combinatorics Test - "The result is invariant"
You actually gave the main idea of the solution.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré
-Henri Poincaré