[Riddler] Horse Races

[Mike]

You have 25 horses. You have a track where you can race five of them at a time. You have no way to measure time, so in each race, you know in what order the horses finished, but not their times. Assuming that all 25 horses do not vary their speeds from race to race, what is the minimum number of races you would need to run to determine which are the three fastest horses?

[Phoebe]

Crap I had what I thought was THE answer and now I think it has to be

[Mike]

Wrong. But close.

[Phoebe]

Is this the smallest number of races that COULD POSSIBLY be held to determine the top 3 fastest horses, or is this the smallest number that have to be held if you want to be certain of the top 3 fastest in any scenario?

[Mike]

The smallest number of races in any scenario that will allow you to determine the 3 fastest horses. And the rules don't specify this, but this method will also tell you the order of those three.

[Phoebe]

I feel like That's the part I'm stuck on.

[Mike]

If you want to know the answer, it is . You have to figure out how to run them, but if you do it right, it works every time.

[Phoebe]

Okay I figured it out, . I have no idea what I was thinking before. High, tired, dementia, or something.

[Mike]

Awesome!