Heya peeps!♡
*answer this with explanations*
There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out how many races are required to get the top 3 horses.
Answers
||✪✪ GIVEN ✪✪||
- Total Number of Horse = 25 .
- we can conduct race of = 5 horse one at a Time..
✯✯ To Find ✯✯
- How many races are required to get the top 3 horses. ?
|| ✰✰ ANSWER ✰✰ ||
From image we can see That, we Divide all 25 Horses with Numbers from 1 - 25 in Group of 5.
Now, we can say That, in First 5 Races , All These horses Run in Group and we can Conclude That :-
→ H1 is winner from Race 1 .
→ H6 is winner from Race 2 .
→ H11 is winner from Race 3 .
→ H16 is winner from Race 4 .
→ H21 is winner from Race 5 .
__________________________
Now, we Have First 5 Winners From all 5 races , we will Arrange Them For 6th race .
→ Race 6 is b/w = H1, H6, H11, H16 & H21.
we conclude That, H1, H6 & H11 are Top 3 in 6th Race.
____________________________
Now we Completed 6 races and we can Conclude That :-
Conclusion ❶ :- From Race 6 we can conclude that, As H16 & H21 comes on 4th and 5th position and in Race 4 & Race 5 They were on Top .. So, we can say That, Horses From Race 4 & Race 5 after H16 & H21 will be not in Top Three.
Or, in Simple words we can say That :- (H17, H18, H19, H20) & (H22, H23, H24, H25) will not be in Final Top three Positions.
Conclusion ❷ :- Now as H11 comes third in the Race 6 , so we can conclude that (H12, H13, H14, H15) cannot be in top 3 positions ..
Or, in Simple words we can say That :- In our final race only H11 will participate and rest all (H12,H13, H14 & H15) need not to participate,, as we are interested in only top 3 fastest horses.
Conclusion ❸ :- As H6 comes second in the Race 6 , so we can be sure that only H7 could have the possibility of third fastest horse.. And rest horses (H8, H9, H10) cannot be on top 3 positions rather they can be at any position between fourth one to last position.
Or, in Simple words we can say That :- In our final race only H6 and H7 will participate and rest all (H8, H9 & H10) need not to participate...
Conclusion ❹ :- As H1 wins the Race 1 and also wins the race with the winner of all rest of the races, That was Race 6.
So, we can Conclude that H1 is the fastest horse among all.
Hence, we do not need to race H1 again with any other horse.
Conclusion ❺ :- As H1 comes first in the race, so we can be conclude that only H2 and H3 could have the possibility of second and third fastest horse respectively and horses (H4 & H5)cannot acquire top 3 positions ...
So, In our final race only H4 and H5 will participate and rest all (H8, H9, and H10) need not to participate ...
Hence, From All These 5 Conclusions we can Conclude That for our final race, we have :- H2, H3, H6, H7, & H11 { For second and third position. }
______________________________
☛ Race 7 :- H2, H3, H6, H7 & H11 ..
Here we will Get Our Next Two Horses For 2nd & 3rd Position.
Let's say H2 and H3 comes at first and second position respectively.
Hence, finally we have top 3 fastest horses in 7 races among 25 horses as: ---
☞ First Position = H1.
☞ Second Position = H2.
☞ Third Position = H3 .
ஃ We Need Minimum ⓻ Races to get the top 3 horses.
______________________________
Answer:
total 3 races are required to get the top 3 horses .
