20171115, 09:28  #1 
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 20171115 at 09:29 
20171115, 09:55  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5·1,223 Posts 
Good puzzle.
I'm going to give it to my minions. Let's see how they progress. 
20171115, 11:46  #3 
"Forget I exist"
Jul 2009
Dumbassville
20300_{8} Posts 
6

20171115, 13:03  #4 
Romulan Interpreter
Jun 2011
Thailand
3^{3}×347 Posts 
Nice puzzle.
The 3seconds solution uses 11 races (no, this does not need a spoiler), the question is how this can be optimized. Thinking...thinking... 
20171115, 13:12  #5 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5,857 Posts 

20171115, 13:43  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5×1,223 Posts 
Hint: It's not too dissimilar to the 12 coins puzzle.

20171115, 14:32  #7  
Jun 2003
11461_{8} Posts 
Quote:


20171115, 15:43  #8  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
10770_{8} Posts 
Quote:
The potential though is that the fastest 3 overall might all be in 1 group (or 2 and 1) 

20171115, 16:16  #9 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2^{3}·5^{2}·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 20171115 at 16:19 
20171115, 16:27  #10 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
10770_{8} Posts 
Ok so only now did I look at the answer from the link posted above.
Quite ingenious....I was sort of getting there. 
20171116, 07:33  #11 
Romulan Interpreter
Jun 2011
Thailand
3^{3}·347 Posts 

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