# Robotic race horses



## robert@fm (Sep 23, 2018)

You have a set of 25 robot racehorses, all of which run at a set programmed speed, and no two run at the same speed. You also have a race track on which you can race up to five horses at a time, and it tells you the order in which the horses finished, but not how fast they finished. You have no other means of checking their speed.

How many races are needed to determine which are the three fastest horses?


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## robert@fm (Sep 23, 2018)

^I forgot to say how _many_ horses you had!  Fixed now, so the puzzle is now solvable.


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## C&E Guy (Sep 25, 2018)

Split the horses into 5 groups of 5. Run 5 races.

Take the 5 winners and race them. Whichever are the last 2 - you can discard those 10 horses as they must be the 10 slowest.  6 races so far.

You have 15 horses left. 

Take the first 3 from each previous race and run them against the slowest 2 from another race. Discard the slowest 6. 9 races so far.

You have 9 horses left.

Run 2 races. A four and a five. Discard the slowest 4. 11 races so far.

You have 6 horses left.

Run Any 5. Discard the last 1. 12 races so far.

You have 5 horses left. By elimination, the 5 fastest.

Race them. Establish the 3 fastest.  13 races.


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## robert@fm (Sep 25, 2018)

It can be done with a lot fewer races than that...


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## mikeyB (Sep 26, 2018)

I reckon it could be done in seven, but there isn’t enough space to show the working out.

You have start as C&E Guy did, to knock out ten, but after that you need pencil and paper to show the logical deductions that you can make if you put the horses in a square array marking their positions. Once you’ve done that, it seems fairly straightforward.

If you tell me I’m wrong, I’ll be devastated.


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