Let $ABC$ be a triangle with its centroid $G$. Let $D$ and $E$ be points on segments $AB$ and $AC$, respectively, such that, $$\frac{AB}{AD}+\frac{AC}{AE}=3.$$Prove that the points $D, G$ and $E$ are collinear. Proposed by Dorlir Ahmeti, Kosovo

Find all polynomials $p(x) \in \mathbb{Z}[x]$ such that for all positive integers $n,$ we have that $p(n)$ is a Palindrome number. Palindrome numbers: A number $q$ written in base $10$ is called a Palindrome number, if $q$ reads the same from left to right, as it reads from right to left. For example : $121, -123321$ are Palindrome numbers, but $113$ is not a Palindrome number. (Proposed by Aditya Guha Roy (India) and Fedor Petrov (Russia))

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that for all real numbers $x$ and $y$, $$(f(x)+f(y))(1-f(x)f(y))=f(x+y).$$ Proposed by Dorlir Ahmeti, Kosovo

Find all integers $n$ such that $2n+1$ is a divisor of $(n!)^2 + 2^n$. Proposed by Silouanos Brazitikos

If $a, b, c$ are real numbers satisfying $a > 1, b > 1, c > 1$, then prove that: $$\frac{a^a}{b^b}+\frac{b^b}{c^c}+\frac{c^c}{a^a}\ge\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$$ Proposed by Aditya Guha Roy

What is the maximum number of subsets of $S = {1, 2, . . . , 2n}$ such that no one is contained in another and no two cover whole $S$? Proposed by Fedor Petrov