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Wizard
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Wizard 
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June 10th, 2017 at 6:00:02 PM permalink
You have 25 horses. You need to determine the three fastest, in order. All you have is a racetrack, which can race five horses at a time. You don't have a watch, so all you know from each race is the top three finishers. Assume that each horse runs at the same speed every race.

What is the least number of races you need to run to determine the fastest three horses, in order, and how should it be done?

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prozema
prozema
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June 10th, 2017 at 6:35:37 PM permalink
I voted 10 but miscounted. I should have said 11. Run a race of 5 and take the top 3. add two more each incremental race. I'm sure this crew will find a more efficient way.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen
Wizard
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Wizard 
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June 10th, 2017 at 6:56:20 PM permalink
Quote: prozema

I voted 10 but miscounted. I should have said 11. Run a race of 5 and take the top 3. add two more each incremental race. I'm sure this crew will find a more efficient way.



Yes, you can correctly get the top 3 that way. However, there is a way to do it with fewer races.
It's not whether you win or lose; it's whether or not you had a good bet.
Johnzimbo
Johnzimbo
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June 10th, 2017 at 7:05:34 PM permalink
I think 9. 5 races with each horse, eliminate the 4th and 5th horse from each race leaves 15 horses. 3 races with those 15 and then one more race with the winners of those three races
prozema
prozema
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June 10th, 2017 at 7:17:17 PM permalink
Quote: Wizard

Quote: prozema

I voted 10 but miscounted. I should have said 11. Run a race of 5 and take the top 3. add two more each incremental race. I'm sure this crew will find a more efficient way.



Yes, you can correctly get the top 3 that way. However, there is a way to do it with fewer races.



we could run 5 heats of 5 to get the top 15. Then run a 6th heat with the winners of each prior heat. That would get us to 6 horses left... Places 1,2,3 for the winner of heat 6... 2 and 3 for the second place finisher, and the 3rd place horse from heat 6. Run a 7th heat of 5 then an 8th heat of 4.

That would do it too I think. 8 races.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen
prozema
prozema
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June 10th, 2017 at 7:23:04 PM permalink
Quote: prozema

Quote: Wizard

Quote: prozema

I voted 10 but miscounted. I should have said 11. Run a race of 5 and take the top 3. add two more each incremental race. I'm sure this crew will find a more efficient way.



Yes, you can correctly get the top 3 that way. However, there is a way to do it with fewer races.



we could run 5 heats of 5 to get the top 15. Then run a 6th heat with the winners of each prior heat. That would get us to 6 horses left... Places 1,2,3 for the winner of heat 6... 2 and 3 for the second place finisher, and the 3rd place horse from heat 6. Run a 7th heat of 5 then an 8th heat of 4.

That would do it too I think. 8 races.



wait... In heat 6, I already know who is first, so I just need a 7th heat of 5 to figure out 2nd and 3rd.

7 is the right answer.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen
Wizard
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Wizard 
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June 10th, 2017 at 7:25:48 PM permalink
Quote: Johnzimbo

I think 9. 5 races with each horse, eliminate the 4th and 5th horse from each race leaves 15 horses. 3 races with those 15 and then one more race with the winners of those three races



That method won't guarantee the fastest three horses. What if the fastest three are all in the first race? The second and third fastest would be eliminated from consideration under your method.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard 
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June 10th, 2017 at 7:28:27 PM permalink
Quote: prozema


wait... In heat 6, I already know who is first, so I just need a 7th heat of 5 to figure out 2nd and 3rd.

7 is the right answer.



Can you elaborate on which horses would be in the 7th race. I'm not sure I understand your solution between the two posts.
It's not whether you win or lose; it's whether or not you had a good bet.
Dalex64
Dalex64
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June 10th, 2017 at 7:30:15 PM permalink

Run 5 races of 5 horses each, all 25 horses are run.

Race #6 is the fastest horse from each of the first five races. Order the first 5 races from the one containing the fastest to the one containing the slowest of the 6th race

Select the 2nd and 3rd place horse from the race with the fastest horse from the first 5 races
Select the 2nd place horse from the heat with the second fastest horse from
Race those three horses with the 2nd and 3rd fastest horse from race 6.

That is race #7.
prozema
prozema
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June 10th, 2017 at 7:34:42 PM permalink
Quote: Wizard

Quote: prozema


wait... In heat 6, I already know who is first, so I just need a 7th heat of 5 to figure out 2nd and 3rd.

7 is the right answer.



Can you elaborate on which horses would be in the 7th race. I'm not sure I understand your solution between the two posts.



the 7th race would be between the 2nd and 3rd place horses from the original 5 heats of the winner of heat 6 plus the top two horses from the original heat of the second place winner of heat 6 plus the 3rd place finisher in heat 6. Hope that makes sense.
"A little luck never hurt any fisherman, that's all I know." - Sig Hansen

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