This is the question:
A reduced copy of a painting by Kandinsky is placed on the top of original. Is there a point of the painting covered by a point of the copy which has the same color? If it is placed upside-down?
I'm completely lost at how to answer this problem. Anyone know? Thanks.
As in my comment above, I take it to mean that 'reduced copy'stands for 'reduced in size but geometrically similar (excluding reflections).'
If that is the case, consider applying some fixed point theorem (e.g., Brouwer's) to show that some point on the reduced copy does sit precisely above the analogous ("same color") point on the original painting.
The map on which the theorem must be applied is $f:D \to D$, where $D\subset\mathbf{R}^2$ is the rectangular domain occupied by the original painting and, for every point $x \in D$ on the original painting, $f(x) \in D$ is the analogous point on the reduced painting. You're in business if you can show that $f$ is continuous. I'll leave that to you, but here's a hint: view the map as the composition of a scaling by some constant &, possibly, a rotation & a translation. (This also helps answer the second part of the problem.)