(To be clear, my matrices are just one possible result, working backwards from knowing the 1st to 16th fastest horse.)

veganray wrote:After heat #1, we know A is faster than B, C, & D

That's reflected as the 13th fastest horse beating 14, 15, and 16th fastest. Okay.

E is faster than everybody else in heat #2 (he won)

That's reflected as the 9th fastest horse beating 10, 11, and 12th fastest. Okay.

I is faster than everybody else in heat #3 (he won)

That's reflected as the 5th fastest horse beating 6, 7, and 8th fastest. Okay.

M is faster than everybody else in heat #4 (he won)

That's reflected as the 1st fastest horse beating 2, 3, and 4th fastest. Okay.

After heat #5, we know that A is faster than E, I, & M

I moved this down into chronological position, and it's reflected as a race between the 1st, 5th, 9th, and 13th fastest horses, with the first horse coming in 1st.

From the results of heat #5, we know that E is faster than I or M

As far as I can tell, this only means that the 5th fastest horse is faster than the 9th or 13th fastest horse.

Therefore we know that E is faster than everybody in heats 2, 3, & 4

That's the trouble spot, it may be that I'm dim and not seeing it, but looking at my example all I can say for sure is that you can be %100 sure that the fastest horse on the track won heat #5. The second, third, and fourth horses were beaten in heat #4 by the fastest horse, but I don't see how they've been accounted for in heat #5?

BTW - if the results of heat #5 were different, we would just rename the first four heats such that heat #5's winner's heat is deemed "heat #1", heat #5's runner-up's heat is deemed "heat #2", heat #5's 3rd place horse's heat is deemed "heat #3", and heat #5's loser's heat is deemed "heat #4".

Heh. I do not understand "we would just rename the first four heats such that heat #5's winner's heat is deemed "heat #1"", apologies for my obtuseness.