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How many heats?


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19 replies to this topic

#1 bonanova

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Posted 26 January 2008 - 11:41 AM

The annual Horse racing tournament is a week away.
You own 25 horses, and you're allowed to enter up to three.
You decide to hold a series of races to find your three fastest horses.
You have access to a track that permits five horses to race against each other.

Here's the deal:

[1] No two of your horses are equally fast - there will be no ties.
[2] You have no stopwatch - you can't compare performances from different heats.
[3] You do not want to tire the horses needlessly - the fewer heats needed, the better.
[4] You want to know which horse is fastest, which is next fastest and which is third-fastest of the 25.

How many heats are needed?
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Vidi vici veni.


#2 brhan

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Posted 26 January 2008 - 03:23 PM

Spoiler for my solution

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#3 PDR

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Posted 26 January 2008 - 04:49 PM

when I read brhan's spoiler I didn't believe it - after all - you need 5 heats just to make sure each horse races once. After much reflection, I now see how it's done - good job brhan!
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#4 unreality

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Posted 26 January 2008 - 05:11 PM

The annual Horse racing tournament is a week away.
You own 25 horses, and you're allowed to enter up to three.
You decide to hold a series of races to find your three fastest horses.
You have access to a track that permits five horses to race against each other.

Here's the deal:

[1] No two of your horses are equally fast - there will be no ties.
[2] You have no stopwatch - you can't compare performances from different heats.
[3] You do not want to tire the horses needlessly - the fewer heats needed, the better.
[4] You want to know which horse is fastest, which is next fastest and which is third-fastest of the 25.

How many heats are needed?


* Split them into five heats. Take the 3 fastest in each heat, meaning you now have the 15 fastest.
* So do 3 heats now. Take the 3 fastest in each heat. You have the 9 fastest horses.
* Do a single heat with 5 random horses of the 9, cutting out the 2 last-place horses, leaving you with 7.
* Take another random 5 horses and do it again, cuttnig out 2, leaving you with 5 horses.
* Do one final heat and take the top 3 from that race.

Those top 3 horses will only have to race 5 times each.
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#5 brhan

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Posted 26 January 2008 - 05:27 PM

* Split them into five heats. Take the 3 fastest in each heat, meaning you now have the 15 fastest.
* So do 3 heats now. Take the 3 fastest in each heat. You have the 9 fastest horses.
* Do a single heat with 5 random horses of the 9, cutting out the 2 last-place horses, leaving you with 7.
* Take another random 5 horses and do it again, cuttnig out 2, leaving you with 5 horses.
* Do one final heat and take the top 3 from that race.

Those top 3 horses will only have to race 5 times each.


Spoiler for my solution

Edited by brhan, 26 January 2008 - 05:28 PM.

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#6 PDR

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Posted 26 January 2008 - 05:46 PM

top horse races twice, 2nd & 3rd race 2 or 3 times max...
Spoiler for here's how

Edited by PDR, 26 January 2008 - 05:46 PM.

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#7 roolstar

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Posted 26 January 2008 - 07:22 PM

Spoiler for Seven Heats!!

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#8 dylangaine

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Posted 22 February 2008 - 03:35 PM

Spoiler for Seven Heats!!


why is the answer not SIX heats? Race 5 heats to get the top 5 horses. Then race the top five horses in the sixth heat. Your fastest three are the horses that finishes first, second and third in the sixth heat.

What am i not seeing?
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#9 brhan

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Posted 22 February 2008 - 03:45 PM

why is the answer not SIX heats? Race 5 heats to get the top 5 horses. Then race the top five horses in the sixth heat. Your fastest three are the horses that finishes first, second and third in the sixth heat.

What am i not seeing?


It is possible that the 3 fastest horses could be in one group. If you only do SIX races, you will leave out the 2nd and 3rd fastest horses because you are only considering (in the sixth heat) the horses that stood first from each group.
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#10 barne012

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Posted 22 February 2008 - 03:53 PM

For more discussion, also check this topic Horse Race, started in June 2007.
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