Question

There are 25 horses and we're looking for the 1st, 2nd, and 3rd fastest horses. We can race the horses 5 at a time. What is the minimum number of races we need to find the fastest horses?

Answer 1

I got 12 races.

Explanation:

Let's number our horses H1 to H25.

Let's now race horses - let's race H1 to H5, H6 to H10, and so on - we'll have 5 races.

From each of those races, we'll take the 1st, 2nd, and 3rd place finishers (because it's possible the 3 fastest horses were all in one race!) - that's 15 horses. And now let's race them again (3 races) and take 1st, 2nd, and 3rd. Now we have 9 horses.

We can now have 2 races, one with 5 horses and one with 4, and take the top three finishers from those. We now have 6 horses.

It'll take 2 races to finish up - we run one race with 5 (have the 6th horse sit out) and take the top three. The last race will have those top finishers plus the horse that sat out a race. We'll then have the top 3 finishers be the fastest 3 horses.

So that's `5+3+2+2=12` races.