Shnol D.e.

In the class, there are 27 students, but not all of them came to the physical education lesson. The teacher divided the students who came into two equal teams to play pioneerball. In the first team, there was half of all the boys who came and a third of all the girls who came, while in the second team, there was half of all the girls who came and a quarter of all the boys who came. The rest of the students who came helped as referees. How many helpers could there have been for the referee?

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From the condition, it follows that the number of girls who came is a multiple of 6, and the number of boys who came is a multiple of 4. Let these quantities be denoted by $6d$ and $4m$ respectively. Since the number of members in both teams was the same, then $2m + 2d = 3d + m$, from which we get $m = d$.

Considering that $6d + 4m < 27$, that is, $10d < 27$, we get $m = d = 1$ or $m = d = 2$.

Since one-sixth of the girls and one-quarter of the boys helped the judge, the number of helpers is $m + d$. Therefore, there were either two or four helpers.

## Answer

2 or 4.