There are 5 racing tracks and 25 horses At a time you can conduct race for 5 horses in the five available tracks What will be the minimum number of trials needed to find out the ultimate winner run? or top three horses.

Of course the "outside the box" answers might be passable, I especially like, "None. If I already chose the fastest three horses, they are the fastest." But mathematically, it's 7, assuming the horses always run at the same speed. Natalya did probably the best job explaining it, but I'll try a different tack (ha!). I encourage you to write this down and cross out the eliminated horses. Assume the 25 horses are named A-Y.

Race 1: A B C D E
Race 2: F G H I J
Race 3: K L M N O
Race 4: P Q R S T
Race 5: U V W X Y

So far, yes, the people saying you can only eliminate 2 horses per race are correct. We've only eliminated the slowest two in each heat thus far. Assume the left-most was the fastest and the right-most was the slowest. Now we race the winners:

Race 6: A F K P U

Now we've added a significant amount of information. Not only can we eliminate P and U, but we eliminate all of the horses that they defeated. We can also eliminate all of the horses that K defeated, but we can't eliminate K itself. For each of those horses, at least A, F, and K are faster. Lastly, we can also eliminate H, because we know for a fact that at least A, F, and G are faster.

We know A is the absolute fastest, so that leaves:

Race 7: B C F G K

The winner and runner up have to be the second and third fastest, respectively.