# Solution to rank the 25 horses puzzle

This is the solution / answer to the puzzle Rank the 25 horses puzzle posted on 23rd March 2008.

Those who havent tried it yet.. Give a try at Rank the 25 horses puzzle

We group the 25 horses in 5 groups each containing 5 horses.In each of first five races we will rank each five horsesA, B,C,D and E ( A : fastest and E: slowest) in the group.

1A 1B 1C 1D 1E

2A 2B 2C 2D 2E

3A 3B 3C 3D 3E

4A 4B 4C 4D 4E

5A 5B 5C 5D 5EIn the sixth race ( among the first of each group) we will get the fastest horse and rank these five horses 1A,2A,3A,4A & 5A (1A : fastest and 5A slowest)

Similarly .just select the fastest of the remaining horses from each row for the race.Now we have got the fastest horse 1A and will also set nomenclature for each horses.

The fastest of the remaining horses in the row will take part.For e.g. the seventh race will be between 1B & 2A (no need to run 3A,4A & 5A)for determining

2nd fastest horse.The 8th race will determine the third place and it will be between 1C and 2B ( in case 1B wins 7th race) or among 1B,2B & 3A ( in case 2A wins 7th race).

The 9th race will determine the 4th place and the 10th race will determine 5th place.

And moving on 25 th race will determine 20th place.The 26th race will tel the remaining 5 ranks.

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can we do better ?

like with the 7th race can tell the 2nd and the 3rd fastest horses. and then proceeding in similar fashion , we get 24 races

so , what will be the minimum number of races required ? any ideas ?

How would 7th race give the third fastest. It can only give us the 2nd fastest.. correct??

@ can we do better ?As i found… this was the best possible solution. Please suggest if any.

the fastest horse is the winner of the 6th race

2nd fastest horse is either the 2nd horse in the winners list , or the 1st horse in 2nd fastest’s list

now 3rd fastest is either the 3rd horse in fastest’s list , or 2nd horse in 2nd fastest’s list , or the 1st horse in 3rd fastest’s list

H11 H12 H13 H14 H15

H21 H22 H23 H24 H25

H31 H32 H33 H34 H35

so , race H12 H13 H21 H22 H31 and we get 2nd and 3rd fastest horses

What r the answers..just the answers!

I had been asked this question in my interview. The answer is: 7 races.

Thanks,

Sanket

the popular solution is wrong because what if the 5 fastest horses were all included in a single race? then you would not end up with the 5 fastest through this method of elimination.