Pretty common I think. At least I have seen it before. Assuming we award gold, silver, bronze medals to first, second, third best competitors respectively. Design a single-knockout tournament. This will determine the winner $A$ in $31$ matches. Suppose $A$ beats $B_1, B_2, B_3, B_4, B_5$ in order from the most recently beaten (met at finals), then the second best person must be one among these people (since the second person wins all his matches until he meets $A$). Create a "second-place tournament": Arrange a match between $B_5, B_4$; the winner goes against $B_3$; the winner goes against $B_2$; the winner goes against $B_1$. This will determine the second placer $B_i$ in $4$ matches. Suppose that $B_i$ beats $C_{i+1}, C_{i+2}, \ldots, C_5$ in order from the most recently beaten (met at the last game before $B_i$ is beaten by $A$). The third placer must be beaten by either $A$ or $B_i$, so he can only be one of the following: The one that $B_i$ beats at $B_i$'s first match in the second-place tournament, one of $B_{i-1}, B_{i-2}, \ldots, B_1$, or one of $C_{i+1}, C_{i+2}, \ldots, C_5$. There are five people here, and it's easy to see that we can determine the winner in $4$ more matches, making the count $39$.