### Brain Teasers

# Madadian Race Horses

Mad Ade's rich uncle "Uncle Rich" owned the famous Madadian Race horse breeding stables "The Gluepot".

It has a private race track that has five lanes.

Uncle Rich has 25 horses and wishes to know which are the three fastest.

What is the least number of races needed to be run to find the answer?

Note that it is only the ranking of the horses being found not the actual timings.

It has a private race track that has five lanes.

Uncle Rich has 25 horses and wishes to know which are the three fastest.

What is the least number of races needed to be run to find the answer?

Note that it is only the ranking of the horses being found not the actual timings.

### Answer

Answer: 7 racesRace #1 to Race #5 - Divide the horses into 5 groups of 5. Race each group to rank the first 3 in each - that's 5 races.

Race #6 - Race the winner from each group. The winner in this race is the fastest horse.

Race #7 - Race the second and third horses from the race in which the fastest horse raced initially,

the first and second horses from the group of the second horse in Race #6, and the third horse in Race #6 (that's a total of 5 horses).

The first and second horses in Race #7 are the second and third horses of the entire stable.

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## Comments

Cute logic. Nice puzzle badly worded. It should say that they cannot be timed, not just merely that we do not need to know the times. Otherwise the answer would be a boring 5 timed races.

Incidentally I was skeptical of the given answer until I drew a matrix. Isn't it lovely how logic can make obvious what plain commonsense sometimes refuses to grasp.

Incidentally I was skeptical of the given answer until I drew a matrix. Isn't it lovely how logic can make obvious what plain commonsense sometimes refuses to grasp.

It does say in the question that the horses are not timed, just their rankings are taken into consideration.

How many racetracks have only 5 lanes???? At most racetracks, any less than 4-5 competitors and a race won't even be run! Otherwise, a good teaser... a little easy though...

they do things a little differently in Madadia...

I still don't get why it wasn't only 6 races... first five, you take the fastest from each.... and put them into the sixth... that's only 5 horses left in that race, and you take the top three??

omega, what u should understand is that even the last horse from winner's 1st round MIGHT be faster than the runner-up in the 2nd round...btw, another great teaser hakken!

Great one.

Here how I came to the solution:

In the following schema we assume we make all the races and then retrospectively put numbers on them the match the order.

First 5 races the results:

01-02-03-04-05

05-07-08-09-10

11-12-13-14-15

16-17-18-19-20

21-22-23-24-25

#6:Now the winners race result:

01-05-11-16-21

From all of the above, only the following could still be on the list.

01-02-03

05-07

11

01 for sure is the total winner, thus we can make a race with the other 5

#7

02-03-05-07-11

this even gives the exact order (which was not asked for)

Here how I came to the solution:

In the following schema we assume we make all the races and then retrospectively put numbers on them the match the order.

First 5 races the results:

01-02-03-04-05

05-07-08-09-10

11-12-13-14-15

16-17-18-19-20

21-22-23-24-25

#6:Now the winners race result:

01-05-11-16-21

From all of the above, only the following could still be on the list.

01-02-03

05-07

11

01 for sure is the total winner, thus we can make a race with the other 5

#7

02-03-05-07-11

this even gives the exact order (which was not asked for)

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