Here's a problem i invented myself, but i'm not sure about my solution. I'll show it later, so people can enjoy trying to find one:
Consider the function $f:\mathbb{R}^2\to\{1,2,...,2012\}$ that satisfies the following rule: If $a, then $f(a,c)=f(b,c)=f(a,b)$ and $f(b,a)=f(c,a)=f(c,b)$.
Let $x_1,x_2,...,x_{2010}$ be a sequence of real numbers, which are all different.
Find the number of possible ordered $2010^2$-tuples
$\Bigl(f(x_1,x_1),f(x_1,x_2),\ldots,f(x_1,x_{2010}),f(x_2,x_1),f(x_2,x_2),\ldots,f(x_2,x_{2010}),\ldots,f(x_{2010},x_{2010})\Bigr)$