Jane Street

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# There are 25 horses. Each time you can race 5 horses together. Now you need to pick the top three horses among them. How many races do you need to conduct?

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I think it is 7. Kannp, the top five are not established after 5 because the second in one race might be better than the first in another race. Have five races of five each and keep the top 3 in each races. Then, take each of the winners and race them against eachother. The two bottom and the 4 who lost to them are discarded. The two who lost to third place is discarded. And, the one who got 3rd in the race with the horse who gets second in the 6th race is discarded. Now, there are six horses left. Race all but the horse who won twice and keep the top two, combined with the horse who sat out. Now you are done in 7 races.

Anonymous on

3

He gave a very good explanation. I'll decline to explain why prm is incredibly wrong.

Ananymous is right on

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7 times.

Anonymous on

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I got stuck with his explanation but once I understood it, it seems very brilliant. Let me put it in this way: 5 groups, each of 5 horses -> race (heat) take the 1st from each group and race (semi-final) discard the 4th and 5th one and all other horses which lost to them in the heat race keep the 3rd one but discard all horses lost to it in the heat race keep the 2nd one but discard the 3,4,5-th horses who raced against it in the heat race keep the 1st one but discard the 4,5-th horses who raced against it in the heat race Now there are 6 horses, namely the 1st from semi-final and the two just following him in heat the 2nd from semi-final and the one just following him in heat the 3rd from semi-final the 1st from semi-final is champion. ignore it and race all other 5 horses in final so 7 in total definitely Russ considers more cases but I am not interested in making it too complicated

Anonymous is right X2 on

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Hey guys, revicing the things here. Can you guys be more explicit on the 7 figure ? Even with the explainations it’s not clear for me. You say run the 5 winners of the 1st round and discard the last 2, but what if the 5 winners of the first round are actually the 5 firsts ?

O. on

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Forget it I read with my eyes closed, I was lookin for top 5 and it’s top 3

O. on

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7 is correct in assumption that each round ends up with a clear 1-st, 2-nd and 3-rd places. If horses can come simultaneously - than we need 11 rounds (When we have 9 horses left - we set up a round for first 5 and set up a round for the last 4 and a horse that took 3-rd place in the previous round. This leaves us 5 horses to race in the final 11th round).

Russ on

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7

Nova on

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1) 5 heats take the first 3 =15 horses left 2) run 3rd against each other, take the first, same thing for 2nd and for the 1st take the best 3 = 3 heats 5 left 3) final heat 9 total

alessandro on

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doesn't that assume that 1st in one race is faster than 2nd/3rd/4th/5th in all the other races? can we be sure of that? 1st round: 25 horses and 5 heats => drop bottom 2 in each race 2nd round: 15 horses and 3 heats => drop bottom 2 again 3rd round: 9 horses and 2 heats => drop bottom 2 from large heat and 1 from the other 4th round: 6 horses and 2 heats; first heat has 5 and drop bottom 2 then race again with the 6th horse included 12 heats in total but there's probably a more efficient way

marty holah on

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you're over thinking this...... run 5 heats with 5 horses in each one. Using a stopwatch, you take the 3 fastest........ but if you don't have a stop watch - anonymous is wrong... marty is right - anonymous you can't take the winner of each race, because you need the top 3. if a 2nd place from one race is faster than the other 4 winners, you don't have it right. 1st time thru 5 horses by 5 heats drop bottom 2 = 15 left 2nd time thru 5 horses by 3 heats drop bottom 2 = 9 left 3rd time thru one race with 5, other with 4. keep top 3 of each race = 6 left now run any 5 horses, keep top 3 and for last one, run remaining 4,drop last. 12 heats total

prm on

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after the 5th race the top five will be established; so, after the 6th the top three could be established. Answer is 6.

Kaanp on