## 25 Horses 5 Tracks Puzzle (Interview Puzzle)

###### 2 years ago Lalit Bhagtani 0

**25 Horses 5 Tracks Puzzle :-** You have given one horse race track and 25 horses. In one race, only(maximum) 5 horses can run together. What is the minimum number of races that are required to find 3 fastest horses?

## Now try to solve this on your own…

## Solution of 25 Horses 5 Tracks Puzzle :-

Let’s divide 25 horses into five different group, containing 5 horses each and name them for easy understanding.

**Group A** :- A1, A2, A3, A4, A5

**Group B** :- B1, B2, B3, B4, B5

**Group C** :- C1, C2, C3, C4, C5

**Group D** :- D1, D2, D3, D4, D5

**Group E** :- E1, E2, E3, E4, E5

**Step 1 :-** Conduct 5 races, one per group to find out 3 fastest horses in each group. Let’s imagine the result of 5 races is :-

**Result of 1st race (Group A) :- **A2 > A4 > A1

**Result of 2nd race (Group B) :- **B1 > B3 > B2

**Result of 3rd race (Group C) :- **C5 > C2 > C3

**Result of 4th race (Group D) :- **D3 > D2 > D5

**Result of 5th race (Group E) :- **E1 > E2 > E3

**Step 2:-** Conduct 1 race between, all the fastest horse of each group. So in this case, the race will be between A2, B1, C5, D3, E1. Let’s imagine the result of this race is :-

**Result of 6th race :- **B1 > C5 > A2 > D3 > E1

By analyzing the result of 6th race, we can say that :-

- B1 comes at 1st position in race 6th, So we are sure that B1 will be in the top 3. Now there is a chance that B3 and B2 can also come in top 3 if they are faster than C5. Hence, we will keep B3, B2 and eliminate B4, B5.
- C5 comes at 2nd position in race 6th and B1 is in top 3. So there is the chance that C5 and C2 can come in top 3 if they are faster than B3 and B2. Hence, we will keep C5, C2 and eliminate C1, C3, C4.
- A2 comes at 3rd position in race 6th. So there is a chance that A2 can come in top 3 if he is faster than B3, B2, and C2. Hence, we will keep A2 and eliminate A1, A3, A4, A5.
- D3 comes at 4th position in race 6th, So there is no way that D3 and rest of the members of his group D can come in top 3 as they all are slower than D3. Hence they all are eliminated.
- E1 comes at 5th position in race 6th, So there is no way that E1 and rest of the members of his group E can come in top 3 as they all are slower than E1. Hence they all are eliminated.

**Step 3 :-** Conduct 1 race between, B3, B2, C5, C2, A2 to find 2 fastest horse. Let’s imagine the result of this race is :-

**Result of 7th race :- B3 > C5 > B2 > C2 > A2**

Hence, 3 fastest horse in 25 horses will be- **B1, B3, and C5** and minimum races require to get 3 fastest horse is **7 races**.

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