There are 25 horses and 5 race tracks how many times (minimum number of times) you need to conduct a race to find the fastest horse?
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So far we have had 5 races. All the horses in red can be eliminated. Any horse that finished below third in it's group race can not be third or higher overall. But we don't know much else, there many possible combinations that could be the fastest three. It could be, in order C1, C2 & C3. A1, B1 & C1 B1, C1 & B2. B1, B2 & C1. But it can't be, in order A1, B1 & C2.
The rule is if a horse is in the top 3 then any horse that came higher in it's group must also be in the top 3 and higher than it. So for C2 to get in to the top 3 then C1 must also be in the top 3 and higher. For C3 to be in the top 3 then both C2 and C1 must also be in the top 3 and higher. Which would mean the top 3 would in fact have to be C1, C2 & C3 in that order.
Time for another race, lets race the top finishing horse from each group, A1, B1, C1, D1 & E1.
We shall assume for convenience that they finish in that order A1, B1, C1, D1 & E1. A1 is now clearly the fastest horse overall.
We're at 6 races.
• If D1 and and E1 are not in the top 3 then by our rules, D2, D3... E2, E3... can't be in either. Which follows.
• As we said before, but only by example in order that C3 be in the top 3 the top 3 would have to be C1, C2 & C3 in that order. It's not so C3 can go.
• Much the same can be said of C2. Since C1 is at best 3rd, (assuming the top 3 were A1, B1 & C1,) C2 can't possibly be in the top 3.
• B3 can be eliminated for the same reason as C3, That the Top 3 can't be B1, B2 & B3 as A1 is fastest.
For our seventh and final race we must test B1, C1, A2, B2 & A3. The fastest of these will be second overall and the second of these will be third over all. Who finishes 3rd, 4th etc in this race does not tell you anything about who is 4th, 5th over .
I'm not sure how clear the diagram below is. The idea is that it shows you the possible combinations. Such as A1, A2 & B1 is possible but A1, A2 & B2 is not.
So the no of races would be 7.
PLEASE MARK AS BRAINLIEST
So far we have had 5 races. All the horses in red can be eliminated. Any horse that finished below third in it's group race can not be third or higher overall. But we don't know much else, there many possible combinations that could be the fastest three. It could be, in order C1, C2 & C3. A1, B1 & C1 B1, C1 & B2. B1, B2 & C1. But it can't be, in order A1, B1 & C2.
The rule is if a horse is in the top 3 then any horse that came higher in it's group must also be in the top 3 and higher than it. So for C2 to get in to the top 3 then C1 must also be in the top 3 and higher. For C3 to be in the top 3 then both C2 and C1 must also be in the top 3 and higher. Which would mean the top 3 would in fact have to be C1, C2 & C3 in that order.
Time for another race, lets race the top finishing horse from each group, A1, B1, C1, D1 & E1.
We shall assume for convenience that they finish in that order A1, B1, C1, D1 & E1. A1 is now clearly the fastest horse overall.
We're at 6 races.
• If D1 and and E1 are not in the top 3 then by our rules, D2, D3... E2, E3... can't be in either. Which follows.
• As we said before, but only by example in order that C3 be in the top 3 the top 3 would have to be C1, C2 & C3 in that order. It's not so C3 can go.
• Much the same can be said of C2. Since C1 is at best 3rd, (assuming the top 3 were A1, B1 & C1,) C2 can't possibly be in the top 3.
• B3 can be eliminated for the same reason as C3, That the Top 3 can't be B1, B2 & B3 as A1 is fastest.
For our seventh and final race we must test B1, C1, A2, B2 & A3. The fastest of these will be second overall and the second of these will be third over all. Who finishes 3rd, 4th etc in this race does not tell you anything about who is 4th, 5th over .
I'm not sure how clear the diagram below is. The idea is that it shows you the possible combinations. Such as A1, A2 & B1 is possible but A1, A2 & B2 is not.
So the no of races would be 7.
PLEASE MARK AS BRAINLIEST
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Answer:
6 race
Step-by-step explanation:
Tip
- To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution. 2 archai : complicate, entangle.
Given
25 horses and 5 race tracks
Find
how many times (minimum number of times) you need to conduct a race to find the fastest horse
Solution
you need to run all 25 horses at least once for finding fastest one and as you can only race 5 horses at a time, then minimum of 25/5 = 5 races. and after that you need to compare the winners of these races, means a 6th race is necessary.
Final Answer
6 races
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