Choosing the Fastest 3 Horses from 25 - No Stopwatch Needed

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Discussion Overview

The discussion revolves around determining the minimum number of races required to identify the fastest three horses out of a group of 25, given that only five horses can race at a time on five available tracks, and no stopwatch can be used.

Discussion Character

  • Exploratory, Debate/contested, Homework-related

Main Points Raised

  • One participant suggests that all 25 horses should race in five separate races of five horses each, implying this is a starting point for the solution.
  • Another participant reiterates the problem statement, indicating a potential need for clarification or further exploration of the solution.
  • Some participants express opinions on the organization of the thread, suggesting that new questions should be posted in separate threads to maintain clarity.
  • Multiple participants provide their own solutions, but the details of these solutions are not disclosed in the provided posts.

Areas of Agreement / Disagreement

There is no clear consensus on the solution, as multiple participants have proposed their own approaches and solutions, indicating that the discussion remains unresolved.

Contextual Notes

Some assumptions regarding the racing format and the criteria for determining the fastest horses may not be explicitly stated, leading to potential variations in proposed solutions.

Who May Find This Useful

Participants interested in problem-solving strategies, combinatorial reasoning, or competitive scenarios may find this discussion relevant.

kaliprasad
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you have 25 horses and you have to pick fastest 3 out of the 25. In each race
only 5 horses can run at the same time as there are only 5 tracks. what is the
minimum number of races to pick the 3 horses without using a stopwatch.
 
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No answer yet so I provide a hint.

of course all 25 horses to run . So there will be 5 races of 5 horses each.
now the hint question

which horses run in 6th race and beyond
 
My solution

you make the horses into 5 groups of 5 horses each say A,B,C,D,E . have 5 races. then pick the winner of the 5 races and have a race that is race number 6.
Now pick the 3 winners out of the 5. Say the winner is from group A, the 2nd ranked is from Group B and 3rd one is from group C.
now let the 1st 3 positions in group A be A1,A2,A3. in group B be B1,B2,B3. and in group C be C1,C2, C3.
A1 is the 1st. B3 cannot be in top 3 beacuse A1, B1, B2 are faster.
So B3 is ruled out.
C2 and C3 cannot be in top 3 as A1,B1,C1 are faster. So have a race among A2,A3,B1,B2,C1 and choose the 2 fastest. the ranks shall be 2nd and 3rd.
So we need 7 races.
 
Last edited:
kaliprasad said:
you have 25 horses and you have to pick fastest 3 out of the 25. In each race
only 5 horses can run at the same time as there are only 5 tracks. what is the
minimum number of races to pick the 3 horses without using a stopwatch.
now I am interested in the following question:
what is the minimax number of races to ensure the 3 horses can be chosen without using a stopwatch ?
 
Albert said:
now I am interested in the following question:
what is the minimax number of races to ensure the 3 horses can be chosen without using a stopwatch ?

IMHO new question should start on a new thread
 
kaliprasad said:
My solution

you make the horses into 5 groups of 5 horses each say A,B,C,D,E . have 5 races. then pick the winner of the 5 races and have a race that is race number 6.
Now pick the 3 winners out of the 5. Say the winner is from group A, the 2nd ranked is from Group B and 3rd one is from group C.
now let the 1st 3 positions in group A be A1,A2,A3. in group B be B1,B2,B3. and in group C be C1,C2, C3.
A1 is the 1st. B3 cannot be in top 3 beacuse A1, B1, B2 are faster.
So B3 is ruled out.
C2 and C3 cannot be in top 3 as A1,B1,C1 are faster. So have a race among A2,A3,B1,B2,C1 and choose the 2 fastest. the ranks shall be 2nd and 3rd.
So we need 7 races.
very good, but there is a flaut, if actural speeds of B3,C2,and C3 are faster than the speeds of A2 and A3
but they did not have a chance for the last trophies competition ,this sounds strange !
 
Last edited:
Albert said:
very good, but there is a flaut, if actural speeds of B3,C2,and C3 are faster than the speeds of A2 and A3
but they did not have a chance for the last trophies competition ,this sounds strange !

we are looking at 1st 3 candiddates c2 and c3 cannot come as A1,B1,C1 all 3 are faster than these.
B3 cannot come in top 3 as at least 3 candidates A1, B2, B1 are faster. Of course 5 fastest re not in race 7 but 2 fastest
and 3 others are in the race as A1 is fastest for sure.
 

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