Yes... you have picked a flaw.
We need to modify
All 25 horses race in 5 heats
The 4th and 5th of each heat eliminated
Race 6 is the winners of the 5 heats.
The first placegetter of race 6 goes through.. (It is THE fastest)
Race 7 is the 2nd and 3rd placegetters of race 6 plus the horses that finished 2nd and 3rd in the heats to the winner of race 6, and the horse that ran second in the heat won by the second placegetter on race 6.
The first and second placegetters in this race,,, plus the winner of race 6 are are 3 qualifyers...
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