You have 25 horses and need to find the 3 fastest ones. To measure relative speeds of horses, you race at most 5 and record the order they finish in (but it is impossible to tell the times of each individual horse).

At least how many races do you have to make to find the 3 fastest horses and why?

  • 11
    $\begingroup$ Technically, all stones will fall at the same speed because the acceleration due to gravity is constant for all objects. $\endgroup$ – user41805 May 13 '17 at 9:57
  • $\begingroup$ @KritixiLithos yep, I was going to tell the same thing :) $\endgroup$ – Oray May 13 '17 at 10:07
  • $\begingroup$ @KritixiLithos With air resistance as a factor they will fall at different speeds even if slight. To illustrate this, try dropping a full milk jug and an empty one at the same time. $\endgroup$ – Web_Designer May 15 '17 at 7:16
  • $\begingroup$ Assuming stones actually fall at different speeds, it is the same as this question. $\endgroup$ – Trenin May 15 '17 at 15:38

I assume you mean measure the force.

7 drops

First five drops would be to drop 1-25 in batches of 5. You get the 5 heaviest stones in their respective pools.

6th drop would be a drop among the five stones winning their respective drops. The heaviest stones is placed aside (on the podium as No 1)

7th drop would be finishers No 2 and 3 of drop 6, No 2 and 3 of the initial​ five drops in which the heaviest stone won and No 2 of drop of the initial give drop in which the runner up of the sixth drop finished first. The top two of drop 7 are the second and third heaviest stones respectively.

Basically the 5 fastest horses in 25 horses problem.

Explanation for drop 7

Since the heaviest stone competed in its initial drop as well as the 6th drop, the 2/3 finishers in both drops are candidates for second and third heaviest. And since the runners​ up of drop 6 finished first in its initial drop, we need to include the runners up from its initial drop as that could be the third heaviest stone. (Read the horses version online for a clearer explanation)

  • $\begingroup$ (1) Congratulations on recognizing this as a trivial variant of the 25 horses problem.  Note that this question has been restated as the 25 horses problem; you might want to reword your answer accordingly.  (2) Your answer appears to be correct, but it is very hard to understand — and I mean understand the words.  For example, I guess that “give” is a typo for “five”.  You might want to edit your answer for clarity.  (3) If you know of a good online explanation of the 25 horses problem, you should link to it. If you copied your answer from elsewhere, you MUST identify the source. $\endgroup$ – Peregrine Rook May 16 '17 at 19:58

Not the answer you're looking for? Browse other questions tagged or ask your own question.