Let $M$ be the set of integer coordinate points situated on the line $d$ of real numbers. We color the elements of M in black or white. Show that at least one of the following statements is true: (a) there exists a finite subset $F \subset M$ and a point $M \in d$ so that the elements of the set $M - F$ that are lying on one of the rays determined by $M$ on $d$ are all white, and the elements of $M - F$ that are situated on the opposite ray are all black, (b) there exists an infinite subset $S \subset M$ and a point $T \in d$ so that for each $A \in S$ the reflection of A about $T$ belongs to $S$ and has the same color as $A$