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 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, 09:55 #2 retina 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.
 2017-11-15, 11:46 #3 science_man_88     "Forget I exist" Jul 2009 Dumbassville 203008 Posts 6
 2017-11-15, 13:03 #4 LaurV Romulan Interpreter     Jun 2011 Thailand 33×347 Posts 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...
2017-11-15, 13:12   #5
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

5,857 Posts

Quote:
 Originally Posted by science_man_88 6
Are you sure? PM me your solution if you can't work out your error

 2017-11-15, 13:43 #6 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 5×1,223 Posts Hint: It's not too dissimilar to the 12 coins puzzle.
2017-11-15, 14:32   #7
axn

Jun 2003

114618 Posts

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

2017-11-15, 15:43   #8
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

107708 Posts

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)

 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
 2017-11-15, 16:27 #10 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 107708 Posts Ok so only now did I look at the answer from the link posted above. Quite ingenious....I was sort of getting there.
2017-11-16, 07:33   #11
LaurV
Romulan Interpreter

Jun 2011
Thailand

33·347 Posts

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.

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