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        riddles >> medium >> Horse Races
        
(Message started by: irrational on Mar 28^th, 2008, 9:38am)

Title: Horse Races
Post by irrational on Mar 28^th, 2008, 9:38am

This may already have been posted, but the search didn't reveal any results so here it is:

There are 25 horses.
In each race only 5 horses can participate.

Q1:
Minimize the races that are required to select best 3 horses out of 25?

Q2:
Minimize the races that are required to select best 5 horses out of 25?

Title: Re: Horse Races
Post by rmsgrey on Mar 28^th, 2008, 10:30am

I can do Q1 in 7 races:

[hideb]race all the horses in the first 5 races, race the 5 winners in the 6th race to establish the fastest overall, then race the 5 remaining horses that could be second and third overall in the last race (the two who came second and third to the overall winner in the initial 5 races, the horse that came second in the sixth race, the horse that came second in the initial 5 races to the horse that came second in the sixth, and the horse that came third in the sixth)[/hideb]

It looks like Q2 can be done in 10, but I'm not sure whether it's possible or optimal.

Title: Re: Horse Races
Post by ima1trkpny on Mar 28^th, 2008, 1:41pm

on 03/28/08 at 09:38:55, irrational wrote:

5 races... use a stopwatch or check the official times ::)
I know you weren't intending in reality LOL but realistically, anything else would be impossible without considering training factors in the weeks between each race as it takes quite awhile to recover the horse and run again.

Title: Re: Horse Races
Post by tohuvabohu on Mar 28^th, 2008, 5:14pm

For Q2, I think I can figure out which are the 5 fastest horses in 8 races, plus a 9th race to put them in order.
I didn't exhaustively check for errors, but my strategy is
[hide]
1-5. Race 5 brackets of 5 horses each.

6. race the 5 second place horses. That should cut the field down to 11 (5 from the winners bracket, 3 from the second place's bracket, and 1 each from the other three brackets.)

7. Then race horse 3 from the winners bracket, horse 2 from the second place bracket, and the other 3 first place horses.
I think that should cut the field down to 7 or 8, depending on the finish order. With at least 3 horses that are in for sure.

8. race the 5 that are unsure to identify the final five.

9. One last race, probably to just get the top 3 horses ranked
[/hide]

Title: Re: Horse Races
Post by tohuvabohu on Mar 28^th, 2008, 5:29pm

And it turns out, it has been asked before:
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1156612286;start=4#4