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You have 9 horses and you have to select fastest 3. You can make a race of 3 horses in one time. So how many time you have to make a race? thanks :-)

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I'm going to guesstimate three races. There will be one winner of each of the three races giving you the three fastest horses of your nine? :)

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@bigpaw - that only gets you the fastest horse in each group. If the groups were arranged so that the three fastest were in the first group then you would eliminate two of the fastest horses in one race. However, Based on the parameters of the question, you only have to run three races. You record the times of each horse then compare them after all horses have raced to determine the three fastest. I presume the actual conditions don't allow timing all of the horses but since you didn't state that then my answer is correct. And, if you ignore bigpaw's second sentence, then he is also correct.

Edited by Reverend Jim

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Hmm.... okay... well, I'll stick with the three races, but as pritaeas highlighted my reasoning was way out.

So, in each of the three races all three horses in each race are timed. You should then be able to determine which of the nine horses are the top three fastest. :)

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@Jim Yup, I'd agree with you there.

I must have been writing my response to pritaeas as you were writing yours to me. We both posted our responses at the same time. Although we're not given a time of when a post was dropped in, both our posts say three hours ago. (at the time of posting this) Why amd I explaining this? I don't want you to think that I am ignoring your comment, We were both telling me that I was wrong at the same time. :)

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But then you'd get the answer.

Applying in-depth psychoanalysis on the word form and articulation of that comment - I'm not so sure he's gonna tell us...

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I think it's at worst six assuming you can't time the horses.

How would the six races be arranged to find the fastest three?

Technically speaking, you would need to be careful of how many races each horse participates in. Depending on how you organise the race, you could exhaust the fastest horse due to repeated racing. The fastest horse could at some point lose to a mediocre horse because it was simply too tired. Or, do they have boundless energy, with some just a little faster than others? (for the sake of the puzzle?) :)

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The races could be spread out over several days to avoid fatigue although other factors cannot be dealt with (eg. tripping & breaking a leg, slipping, differences in jockeys, mood/health differences etc...) but since this is a hypothetical puzzle we can probably ignore those factors.

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Maybe three?

[h1 h2 h3 h4 h5 h6 h7 h8 h9]

Race 1: [h1 h2 h3] -> hi = 1st place finisher
Race 2: [h4 h5 h6] -> hj = 1st place finisher
Race 3: [h7 h8 h9] -> hk = 1st place finisher

[hi, hj, hk] would be the 3 fastest horse?

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As a start, divide the horses into three groups (A,B,C) and race them giving

A1 A2 A3
B1 B2 B3
C1 C2 C3

Now race A1,B1,C1 to get the fastest horse. Next race A2, B1 and C1 to get the second fastest horse. That gets us most of the way there.

And I think we are supposed to assume all horses run at the same individual speed in every race (no horses get tired).

Edited by Reverend Jim

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How many races are you suggesting it would take to determine the fastest horses?

I wonder if just one race would do? You could arrange a Relay Race. A timer still hasn't been ruled out by the questioner, so the fastest horses would be seen in a short period of time. The rules are being held to because only three horses will be racing at each stage of the Relay Race.

Is this puzzle now solved? :)

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As stated, it all depends on the preconditions. So, if the races are timed and all horses will run at the same speed all the time: 3 races will suffice. If you cannot time them, you would need at most 504 races, still based on the assumption that a horse's speed will be identical in every race. The point of this exercise is not identifying the actual number of races (you can't without more information), but the methods of determining the possibilities.

Edited by pritaeas

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You have 9 horses and you have to select fastest 3. You can make a race of 3 horses in one time. So how many time you have to make a race? thanks :-)

I've been working on the premise that there is an answer. Isn't this what the question suggests? :)

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without knowing any other conditions, you cannot calculate the result

I disagree. I got as far as determining the fastest two horses. I just didn't carry it through to the end.

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You may, but I quote:

And I think we are supposed to assume all horses run at the same individual speed in every race (no horses get tired).

That's another condition IMHO. If that were true, on your logic, the answer would be 504.

Edited by pritaeas

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My logic (so far) determined the fastest two horses in five races. That would require at the most four more races to get the third fastest. Three races with 3, 2 and 2 horses, then one more to race the winners of each. So that gives me a maximum of nine races, not 504.

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Now race A1,B1,C1 to get the fastest horse. Next race A2, B1 and C1 to get the second fastest horse

C1 can win both. Says nothing about #2. (unless I missed a post.)

Edited by pritaeas

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If you want the wordier explanation...

Race three groups of three horses to determine the fastest horse in each group. Race the winners of those three races to determine the fastest horse. Next, race the two slower horses from race 4 against the remaining two horses in the group from race 1 that won race 4. Repeat this process with the remaing groups of 3, 2 and 2.

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I agree on finding #1. #2 needs one race, the fastest remainders of each group. Same for #3. After that you may only have to race two at a time (allowed since it is stated you CAN run three, not MUST). Minimal number of races would then be 9, max 11, depending on if one group beats an entire other group, which would exclude some races because you already can predict the remaining order. (Re-racing two from the same group makes no sense, since you can predict the outcome.) Even in this situation, you make the assumption that you can group and recognize your horses, which is not mentioned in the original question.

Edited by pritaeas: Oops

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Even in this situation, you make the assumption that you can group and recognize your horses, which is not mentioned in the original question.

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."
(Sherlock Holmes - who wasn't actually a real person, so, Sir Arthur Conan Doyle)

If something hasn't been ruled out, then it can be factored in. The use of a timer is appropriate, and its use in a relay race would mean that just one race would do the job in identifying the top three fastest horses. :)

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My obvious mistake in the previous post was that you can't race four horses at once. I need some more thought about this.

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