We construct two required groups $G_1$ and $G_2$ as follows: we choose the smallest number on each card and put it in the group $G_1$. Therefore, every card contains at least one number from $G_1$. All other numbers we put in the group $G_2$. Since there are no adjacent cards, the largest number in any card does not coincide with the smallest number on other cards, so this largest number belongs to $G_2$. Therefore, every card contains at least one number from $G_2$.