MHB Choosing the Fastest 3 Horses from 25 - No Stopwatch Needed

[kaliprasad]

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.

 

[kaliprasad]

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

Spoiler

which horses run in 6th race and beyond

 

[kaliprasad]

My solution

Spoiler

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.

 

[Albert1]

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.

Spoiler

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 ?

 

[kaliprasad]

Spoiler

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

 

[Albert1]

My solution

Spoiler

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.

Spoiler

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 !

 

[kaliprasad]

Spoiler

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 !

Spoiler

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.