Qua locus

Keeping both eyes on the long game.

Horse races

Two puzzles involving horses and racing…

You have 25 horses and a track that you can race up to 5 horses on at a time. You cannot time the races, but the horses do not get tired. What races should you run to minimise the total number of races you need to identify the 3 fastest horses?

You now have a different set of 16 horses and the same 5 horse track. Otherwise all else is as before. What races should you run to minimise the total number of races you need to identify the 4 fastest horses?


Written by CGF

July 24, 02012 at 21:24

Posted in Puzzles

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4 Responses

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  1. Going to go with 7 for the first question and 5 for the second. Haven’t fully proved the second part to myself yet, but fairly certain it’s good.

    Edward Moores

    July 25, 02012 at 09:28

  2. Wanted to give others a chance to work them out!

    But the first looks something like this:

    Group the 25 into 5s, and race them off. 5 races, 1,2,3,4,5.

    Winner of each race into a new race Race 6. Let’s say for simplicity winner of race 1 wins, 2 comes 2nd, etc.Therefore can eliminate all of the horses in races 4 and 5 as they all have at least 3 horses faster than them. Similarly can eliminate 2nd through 5th in race 3, and 3rd through 5th from race 2 and 4th and 5th in race 1.

    That leaves us with top 3 of race 1, top 2 of race 2 and top 1 of race 3. However, the winner of race 1 is fastest horse overall, so no need to race again and can sit out of the final (race 7) where we have 5 horses to race – top 2 are 2nd and 3rd.

    Proof of the second question v similar, but with many more options involved. Difficulty comes in the odd numbers and the remaining horses.

    Edward Moores

    July 26, 02012 at 09:50

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