25 horses

henryzz · 2017-11-15, 09:28

You have 25 mechanical horses. You want to find the fastest 3. You can only race 5 at a time and have no stopwatch. How many races do you need?

Bonus puzzles:
1. With the answer to the main puzzle being x, out of how many horses can you find the fastest 3 with x+1 or x+2 races?

2. How many races are needed to find the fastest 4 out of 25 horses? Can this solution work on more horses than 25?

3. Your race track breaks and now you can only race 4 horses at once. How many races are now needed to find the fastest 3 out of 25 horses?

4. Can you work out formulas for any of the above as you vary any of the parameters(fastest 3, 25 horses, racing 5 at once)?

Please use spoilers so others can answer.

retina · 2017-11-15, 09:55

Good puzzle.

I'm going to give it to my minions. Let's see how they progress.

science_man_88 · 2017-11-15, 11:46

6

LaurV · 2017-11-15, 13:03

Nice puzzle.
The 3-seconds solution uses 11 races (no, this does not need a spoiler), the question is how this can be optimized. Thinking...thinking...

henryzz · 2017-11-15, 13:12

Quote:

Originally Posted by science_man_88

6

Are you sure? PM me your solution if you can't work out your error

retina · 2017-11-15, 13:43

Hint: It's not too dissimilar to the 12 coins puzzle.

axn · 2017-11-15, 14:32

Quote:

Originally Posted by henryzz

You have 25 mechanical horses. You want to find the fastest 3. You can only race 5 at a time and have no stopwatch. How many races do you need?

You do a forum search on horse, because it has been asked before and you find this thread: www.mersenneforum.org/showthread.php?t=1048

petrw1 · 2017-11-15, 15:43

Quote:

Originally Posted by henryzz

Are you sure? PM me your solution if you can't work out your error

This would be the scenario where you race 5 groups of 5; take the fastest from each race and race off those 5 to get the 3 fastest.

The potential though is that the fastest 3 overall might all be in 1 group (or 2 and 1)

petrw1 · 2017-11-15, 16:16

This makes sense to me; a little bit of intuition but mostly based on my understanding of Math. Though I can't quite prove it eloquently.

Round 1:
5 Races of 5
Random selection

Round 2:
3 Races of 5
Race 1: 1st from each round 1 race.
Race 2: 2nds
Race 3: 3rds.

Round 3:
1 Race of 5.
Top 3 from Race 1 in Round 2
Top 2 from Race 2 in Round 2
Top 1 from Race 3 in Round 2.

OOPS there are 6 in Round 3.....ummmmmmmmmmmmmmmm

I think we are safe taking only the top from Race 2 of Round 2

petrw1 · 2017-11-15, 16:27

Ok so only now did I look at the answer from the link posted above.

Quite ingenious....I was sort of getting there.

LaurV · 2017-11-16, 07:33

Quote:

Originally Posted by petrw1

Ok so only now did I look at the answer from the link posted above.
Quite ingenious....I was sort of getting there.

Same here, looked to the solution before solving it.

2017-11-15, 09:28	#1
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 5,857 Posts	25 horses You have 25 mechanical horses. You want to find the fastest 3. You can only race 5 at a time and have no stopwatch. How many races do you need? Bonus puzzles: 1. With the answer to the main puzzle being x, out of how many horses can you find the fastest 3 with x+1 or x+2 races? 2. How many races are needed to find the fastest 4 out of 25 horses? Can this solution work on more horses than 25? 3. Your race track breaks and now you can only race 4 horses at once. How many races are now needed to find the fastest 3 out of 25 horses? 4. Can you work out formulas for any of the above as you vary any of the parameters(fastest 3, 25 horses, racing 5 at once)? Please use spoilers so others can answer. Last fiddled with by henryzz on 2017-11-15 at 09:29

2017-11-15, 16:16	#9
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 2³·5²·23 Posts	9 races This makes sense to me; a little bit of intuition but mostly based on my understanding of Math. Though I can't quite prove it eloquently. Round 1: 5 Races of 5 Random selection Round 2: 3 Races of 5 Race 1: 1st from each round 1 race. Race 2: 2nds Race 3: 3rds. Round 3: 1 Race of 5. Top 3 from Race 1 in Round 2 Top 2 from Race 2 in Round 2 Top 1 from Race 3 in Round 2. OOPS there are 6 in Round 3.....ummmmmmmmmmmmmmmm I think we are safe taking only the top from Race 2 of Round 2 Last fiddled with by petrw1 on 2017-11-15 at 16:19

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