# Horse Race Puzzle

There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 horses in a single race to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out minimum number of races are required to find the 3 horses.

The **answer is 7** .Here’s how :

Divide the horses into group of 5 (A,B,C,D,E) and conduct 5 races to find 5 fastest horses .

Now conduct a race among these to find the fastest horse (Let’s say it’s from group E) .and let’s also assume that fastest horse from group D came 2nd and C came 3rd. Total **6 races done**. Now the second fastest horse can be the one who came second in the group E which gave us the fastest horse or the one which came second in 6th race. Similarly the 3rd fastest horse can be

the either fastest horse from group D and C ,or the horses which came 2nd and 3rd in group E or the horse which came second in group D. Conduct a race among these 5 horses and you will **get the result in final and 7th race**.

**My answer** is **11**.

First you split the 25 horses into 5 groups of 5. The puzzle tells us that we **can’t measure speed**, only relative speed, so we** can’t compare horses across races**. Thus, we have to take the top 3 horses of each race. (5 races)

Next, we have 15 horses so we split them into 3 groups of 5. We again take the top 3 of each group. (3 races)

Then, from the remaining 9, we form one group of 5 and take the top 3, adding it to the remaining 4. (1 race)

Now we have 7 remaining, we form another group of 5 and take the top 3, adding it to the remaining 2. (1 race)

We now have 5 horses left and we can form our top 3 in this final race. (1 race)

Add them up and you’ve got 11 races.

The reason I disagree with the first answer:

Imagine a scenario where 3 horses of race #2 are faster than the fastest horse of race #1. You’ve eliminated the 2nd and 3rd fastest horses.

You have to assume the horses will not tire, which is not realistic. Any way, you would race horse # 1 with horse # 2 and the winner would race horse #3. The winner of that race then races horse #4. And so on down the line until horse # 25 races. Minimum # of races is 26.

### Your Answer

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