Task 1 - 091241
At an international camp, a group of 30 friends are participating, some of whom speak German, some Russian, and some French. Some friends speak only one language, some two languages, and some even all three languages.

The number of friends who speak exactly two languages is more than twice but less than three times the number of those who speak only one language. The number of participants who speak all three languages is the same as the number of those who speak only one language.

The number of friends who speak only German is greater than the number of those who speak only Russian, but less than the number of those who speak only French. The number of those who speak only German is less than three times the number of those who speak only Russian.

Give the number of all participants in this group who speak only German, only Russian, only French, and all three languages!
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Let \(s_{1}, s_{2}, s_{3}\) be the numbers of friends who speak exactly one, two, and three languages, respectively. According to the problem statement, we have

(1) \(s_{1}+s_{2}+s_{3}=30\)

(2) \(2 s_{3}6\).

Thus, \(s_{1}=s_{3}=7\) and \(s_{2}=16\).

Let \(d, f, r\) be the numbers of friends who speak only German, French, and Russian, respectively. It follows that \(d+r+f=s_{1}=7\).

Furthermore, from the problem statement, we have \(r<d<f\) and \(d<3 r\).

A simple case distinction shows that this can only be satisfied if \(d=2, r=1\) and \(f=4\). \(\left(s_{3}=7\right.\), see above. \())