I got it on my first guess, but it's still completely unrelated to the problem at hand.
The "25 horses" question is much less useful, but gives you an idea of how the candidate approaches a problem. Getting the right answer is great, but seeing that someone understands the concept of combinatorics or some kind of process of elimination is much more valuable.
You really want a technical question so that you can see someone CODE the solution, or better yet, give them some task to do that's apropos - that part of the argument is fair. In past companies we've done all three, weeding out terrible candidates with the coding questions, weeding out mediocre candidates with thought-process questions, and selecting only the best with a programming simulation.
(echo 'ZW5naW5lZXJpbmdAcm9ja3RoZXBvc3QuY29t' | base64 -D if you're curious, and the answer to the horse problem is 7 IIRC)
Then they would be closer to the fastest horse in there race than any of the horses in the 6th race. Think of it as a calibration step so you can find the positions of every horse by comparing how close they where to the finish line with how close the winner was to the finish line in the final race. (adjusting for a fractionally shorter race as in you don't know it took an minute or an hour but with 98% of the time they got to x so if they had been in the 6th race they would have ended up at y.)
PS: I am treating this as a real world trick question, if your talking about a virtual world where the only information is a horses rank then yea you would need a 7th race with 5 horses assuming no ties.
I've been around that sort of text long enough to know exactly what I'm seeing and respond accordingly. They might be looking at it like that.