Problem - 04 - National Math Camp 2021 Combinatorics Test - "Alternating Parity"
- Anindya Biswas
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Let $n\geq1$ be an integer. A non-empty set is called “good” if the arithmetic mean of its elements is an integer. Let $T_n$ be the number of good subsets of $\{1,2,3,\cdots,n\}$. Prove that for all integers $n$, $T_n$ and $n$ leave the same remainder when divided by $2$.
"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 - 04 - National Math Camp 2021 Combinatorics Test - "Alternating Parity"
I couldn't solve it myself . But since no one is posting the answer I am doing it.
This problem came in the Putnam-2002(A3)
This problem came in the Putnam-2002(A3)
Last edited by Mehrab4226 on Mon May 03, 2021 9:21 pm, edited 1 time in total.
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
- Mehrab4226
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Re: Problem - 04 - National Math Camp 2021 Combinatorics Test - "Alternating Parity"
After seeing the solution, I was like "Keno parlam na!!!"
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