There are 25 horses with different speeds. My goal is to rank all of them, by using only runs with 5 horses, and taking partial rankings. How many runs do I need, at minumum, to complete my task?
As a partial answer, I know that is possible to determine the first 3 horses with 7 runs, and, by a slight generalization of the optimal algorithm used to find the first three, have the complete ranking in 20 runs.
Is it possible to do better?
What if we have n horses and want to rank them with runs with k horses?