Problem 1. In an orthogonal coordinate system $x O y$ a set consisiting of 2000 points $M_{i}\left(x_{i}, y_{i}\right)$, is called "good" if $0 \leq x_{i} \leq 83,0 \leq$ $y_{i} \leq 1 \quad i=1,2, \ldots, 2000$ and $x_{i} \neq x_{j}$ for $i \neq j$. Find all natural numbers $n$ with the following properties: : a) For any "good" set some $n$ of its points lie in a square of side length 1 .

b) There exists a "good" set such that no $n+1$ of its points lie in a square of side length 1 .

(A point on a side of a square lies in the square).