If the total number of points is $y$, then:

$$
\frac{y(y-1)}{2}=136
$$

from which

$$
y_{1}=17, y_{2}=-16
$$

If one group has $x$ points, then the other has $(17-x)$; according to the problem:

$$
\frac{x(x-1)}{2}+\frac{(17-x)(16-x)}{2}=66
$$

from which

$$
x_{1}=10, x_{2}=7
$$

Therefore, one group has 10 points, and the other has 7 points.

(Székely Andor, Unit. Gymn. VIII. grade, Kolozsvár, Unit. Gymn.)

The problem was also solved by: Arnstein K., Bálint B., Bärtl T., Bauss O., Devecis M., Eislitzer Gy., Freibauer E., Freund A., Freund E., Goldstein Zs., Goldziher K.; Grünhut B., Hofbauer E., Kántor N., Kreiszler Gy., Kornis Ö., Kunsch M., Lichtenberg S., Mayer G., Schiffer H., Spitzer Ö., Szabó I., Weisz Á., Weisz J.
In the plane, there are two groups of points. The sum of the lines connecting the groups is 66; the number of lines connecting the points within the groups is 136. How many points are there in each group?