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General math problems
wimpykid   2
N 2 hours ago by whwlqkd

$\textbf{Problem 1}$ In an equilateral triangle of $\frac{n(n + 1)}{2}$ pennies, with $n$ pennies along each side of the triangle, all but one penny shows heads. A $move$ consists of choosing two adjacent pennies with centers $A$ and $B$ and flipping every penny on line $AB$. Determine all initial arrangements - the value of $n$ and the position of the coin initially showing tails - from which one can make all the coins show tails after finitely many moves.

$\textbf{Problem 2}$ Find all functions $f:\mathbb{N} \rightarrow \mathbb{N}$ such that
$$f(f(f(n))) + f(f(n)) + f(n) = 3n$$for all $n\in \mathbb{N}$.
2 replies
wimpykid
4 hours ago
whwlqkd
2 hours ago
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