6. Variant 1.

An artistic film with a duration of 192 minutes consists of four parts. It is known that the duration of any two parts differs by at least 6 minutes. What is the maximum duration that the shortest part can have? Express your answer in minutes.
Answer: 39.

Solution. Let the shortest part be $x$ minutes, then the second (in terms of duration) is no less than $x+6$, the third is no less than $x+12$, and the fourth is no less than $x+18$. Therefore, the entire film lasts no less than $4 x+36$ minutes. Solving the inequality $192 \geq 4 x+36$, we get $x \leq 39$. The durations of the parts being 39, 45, 51, and 57 minutes fit.