You have been charged with finding the 3 fastest horses out of a group of 25. Yo

ID: 3865088 • Letter: Y

Question

You have been charged with finding the 3 fastest horses out of a group of 25. You also need to know which is first, second, and third. You know that any given horse always finishes a race in exactly the same amount of time. You also know that the horses' times are unique (i.e., no two horses ever tie.) You have a racetrack in which you can race up to 5 horses per race. The problem: You are charged 25 dollars per race, and you do not have a stopwatch. You are only able to record the relative positions for each race. (Which horse came in first, second, third, fourth, or fifth?) Find an arrangement of races in which the cost out of your pocket is minimized, and where you always succeed in finding the first, second, and third fastest horses.

Explanation / Answer

We have 5 Track

We have total 25 Horse

Make Group 5 in Each

Group 1:- H1, H2, H3, H4, H5

Group 2:- H6, H7, H8, H9, H10

Group 3:- H11, H12, H13, H14, H15

Group 4:- H16, H17, H18, H19, H20

Group 5:-H21, H22, H23, H24, H25

We have 5 races of 5 horses each, so each row in the group above represents a race.

Let in each race fastest to slowest is left to right side in-group.

In Group 1, H1 fastest, H2 second fastest, H3 third Fastest, H4 is second last in race, H5 is slowest.

In Group 2, H6 fastest, H7 second fastest, H8 third Fastest, H9 is second last in race, H10 is slowest

In Group 3, H11 fastest, H12 second fastest, H13 third Fastest, H14 is second last in race, H15 is slowest

In Group 4, H16 fastest, H17 second fastest, H18 third Fastest, H19 is second last in race, H20 is slowest

In Group 5, H21 fastest, H22 second fastest, H23 third Fastest, H24 is second last in race , H25 is slowest.

The 5 five fastest horses from each race (H1, H6, H11, H16, and H21).

But this is not our answer, because it may be happen H1, H2, H3, H4, H5 are the fastest horse.

H1, H6, H11, H16, and H21 are all the fastest horses in their individual groups.

We have to found only top three so we can eliminate last horse from each group.

H1, H2, H3

H6, H7, H8

H11, H12, H13

H16, H17, H18

H21, H22, H23

Now we do race those 5 horses against each other (H1, H6, H11, H16, and H21) and it would be our 6th race.

Again let’s say that the 3 fastest in that group are H1, H6, and H11

So H16 and H21 are not in the top 3(We eliminate them)

Important:-

As we already eliminated H16 and H21 so, H17, H18, H22, H23 are automatically eliminate

Because H16 is fastest from H17, H18 and H21 is fastest from H22, H23

From Above scenario, we have fastest horse H1

Here if H6 and H11 are the 2nd and 3rd fastest in the group leaders, then we should be able to eliminate H8 since H6 raced against him and he was in 3rd place in that race.

We can also eliminate H12 and H13 since H11 was the 3rd fastest in the group leaders

Now we have to do 7th race between

H2, H3, H6, H7, H11

From this race we will find second and third position

Total 7 races

First: H1

Second : H2

Third:- H3

total cost = 25*7= $ 175

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If you have any query, please feel free to ask.

Thanks a lot.

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