what method should I use ?

Question

There are 25 ducks, each duck having different running speeds. What is the minimum number of duck races required to determine the 3 fastest ducks with the provisions of every duck race followed by 5 ducks and observers are prohibited from using the timekeeper.

Answer 1

Does your statement every duck race followed by 5 ducks mean that 5 ducks per heat is a limitation? (That would be better wording).

five heats: a single winner woild NOT be sufficient to determine 5 ducks to participate in a final heat because it COULD happen that the (ultimately) three fastest were in a single first round heat.

Therefore, from each heat of 5 ducks, keep three top finishers.
So the five heats (ea. with 5 ducks participating) would yield 15 possible candidates for the next round of heats.
This second round of heats, 5 ducks per heat, would have 3 heats, and 3 top ducks from each would be selected.

This brings us to 9 candidates; next round has two heats, each heat selecting 3 candidates. (First heat of this round has 5 ducks racing, 2nd heat has 4 other ducks racing).

And from this most recent heat, there are now 6 candidates, so have one heat, 5 racing, and choose the top three finishers. The duck left out is now ready to go to the final heat, in which 4 participate, and thus the top 3 speedsters can be identified.

Review this--if agreed, count up the total number of heats, including the final one having four finalists.