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?
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.