There are 25 horses and 5 race tracks. We have to pick the fastest three horses in the least no of races. PS: In one race only 5 horses can participate. Find the least number of races?
first pehle 25 horses 5 tracks me dodaye jaynege aur unmese jo pehle aayenga ushe last track 6 me dodayenga right aur ushe race me first three milenge...
suppose in the first race, you get the top runners overall. Unlikely, but possible. With only 6 races, you you definitely get the top ONE, but not the top THREE.
Pick 5 Horses for race, after race replace the slowest with new 1 from the remaining 20. Perform the race again, replace the slowest with new 1 from the remaining 19 and so one continue until all of them get a chance i.e total 21 races to decided the top 5 fastest. 21 = 1 race for 5 + 20 with 1 replacement each.
In First 5 races, we number the horses according to their position. 1 2 3 4 5 - R1 (Race 1) 1 2 3 4 5 - R2 (Race 2) 1 2 3 4 5 - R3 (Race 3) 1 2 3 4 5 - R4 (Race 4) 1 2 3 4 5 - R5 (Race 5)
In Next race we take topmost horse from each previous races, to get fastest horse. But we will also mark 2nd and 3rd position of horses in the 6th race.
Let us suppose the result is R1 - first R4 - second R5 - Third
We can safely remove all horses of R2 and R3. Because if their top most horse is not able to finish in top 3, there is no chance that there other horses will be in top 3.
Now in next race there will be only 3 horses.
Second horse from R1 Top horse from R4 Top horse from R5
After this race we will get second topmost horse. (Race no 7) If top most horse in this race is Second horse from R1 then next race will be in between
Third horse from R1 Top horse from R4 Top horse from R5
If top most horse in this race is Top horse from R4( Similarly for R5) then next race will be in between
Second horse from R1 Second horse from R4 Top horse from R5
After this race( Race 8 ) we will get the Third topmost horse.
You can also take some other combinations also in the above, but for all combinations the answer will be 8 races.Correct me If I am wrong.
if you have timers and a sheet of paper, the answer is 5. Record the times taken by each horse and find the top 3.
Otherwise,
Run set of 5 horses and pick the top 3 in each lot. So now we got 15 horses to compare. Repeat the step, and we will narrow down to 9 horses. Repeat again and we will narrow down to 6 horses. Repeat it with first 5, and run the left alone horse with the third place horse in the first lot. Now we got our top 3. Number of steps: 5(25horses) + 3(15horses) + 2(9 horses) + 2(6 horses) = 12 races.
6 races
ReplyDeletefirst pehle 25 horses 5 tracks me dodaye jaynege aur unmese jo pehle aayenga ushe last track 6 me dodayenga right aur ushe race me first three milenge...
6
ReplyDeleteOnly 5 races are enough. Time will tell you.
ReplyDeletenot always right
ReplyDeletesuppose in the first race, you get the top runners overall. Unlikely, but possible. With only 6 races, you you definitely get the top ONE, but not the top THREE.
but i don't know the answer :-(
11
ReplyDeletePick 5 Horses for race, after race replace the slowest with new 1 from the remaining 20. Perform the race again, replace the slowest with new 1 from the remaining 19 and so one continue until all of them get a chance i.e total 21 races to decided the top 5 fastest.
ReplyDelete21 = 1 race for 5 + 20 with 1 replacement each.
The problem is like external merge sort. so following the above procedure, 11 races are required to get 3 fastest horses...
ReplyDelete8 races.
ReplyDeleteIn First 5 races, we number the horses according to their position.
1 2 3 4 5 - R1 (Race 1)
1 2 3 4 5 - R2 (Race 2)
1 2 3 4 5 - R3 (Race 3)
1 2 3 4 5 - R4 (Race 4)
1 2 3 4 5 - R5 (Race 5)
In Next race we take topmost horse from each previous races, to get fastest horse. But we will also mark 2nd and 3rd position of horses in the 6th race.
Let us suppose the result is
R1 - first
R4 - second
R5 - Third
We can safely remove all horses of R2 and R3. Because if their top most horse is not able to finish in top 3, there is no chance that there other horses will be in top 3.
Now in next race there will be only 3 horses.
Second horse from R1
Top horse from R4
Top horse from R5
After this race we will get second topmost horse. (Race no 7)
If top most horse in this race is Second horse from R1 then next race will be in between
Third horse from R1
Top horse from R4
Top horse from R5
If top most horse in this race is Top horse from R4( Similarly for R5) then next race will be in between
Second horse from R1
Second horse from R4
Top horse from R5
After this race( Race 8 ) we will get the Third topmost horse.
You can also take some other combinations also in the above, but for all combinations the answer will be 8 races.Correct me If I am wrong.
detailed explanation is given in that blog...
ReplyDeleteif you have timers and a sheet of paper, the answer is 5. Record the times taken by each horse and find the top 3.
ReplyDeleteOtherwise,
Run set of 5 horses and pick the top 3 in each lot.
So now we got 15 horses to compare.
Repeat the step, and we will narrow down to 9 horses.
Repeat again and we will narrow down to 6 horses.
Repeat it with first 5, and run the left alone horse with the third place horse in the first lot.
Now we got our top 3.
Number of steps: 5(25horses) + 3(15horses) + 2(9 horses) + 2(6 horses) = 12 races.
7 races...
ReplyDelete5+1+1=7
five races for top three in each group
sixth race for fastest
seventh race for second n third
7 races....
ReplyDelete