I have a question that seems easy at first look, but it's not.
Let's say we have n dimension space. There is a sphere of 1 radius. Now we divide space on dots equaly on a distance $\varepsilon$. You can imagine it like squares in school notebook.
Here is graphical representation in 2 dimensions
The question is how many points (intersections of lines in school notebook representation) lie in sphere?
In other words if we have such formula: $\sum_{i=1}^nx_i^2\le1$ Each of $x_i$ lies in interval $[-1;1]$ divided on equal segments with $\varepsilon$ length. Then how many sets of n values of $x_i$ can we give that inequality is true.