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A riddle
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DaveSimmons
Elite Member
Nice work, this is deterministic / guaranteed, unlike DrPizza's.
Electric Amish
Elite Member
You can't guarantee that any of the horses in the next race(s) are faster than the slowest 2 that you eliminated in the first race...
cKGunslinger
Lifer
I think I understand what you are saying, but I still come up with 11 doing it in my head.
edit: D'oh. I got it now. You can drop out whole groups based on the winners in that race losing to the 3 others. Nice work!
cKGunslinger
Lifer
So? If none of them are, then you already have the 3 fastest horses. Those 2 you eliminated have shown that thre are at least 3 other horses that can beat them, so they are totally eliminated.
DaveSimmons
Elite Member
It works since you're only looking for 3. The first five races are each separate groups (1-5, 6-10, 11-15) and you drop the 2 slowest from that group. You're left with 3 from each group = 15.
Then FuryLine's followup post shows how to eliminate 2 groups of 3 in the next race since the fastest from each group is raced you know the other 2 in each group are slower still.
chuckywang
Lifer
8 races:
First, 5 races of 5 horses each. Eliminate the bottom 2 horses of each race. You are left with 15 horses.
Second, race the 5 winners of the first 5 races. Eliminate the bottom 2 of that race and every horse in their group from their first race. You are left with 9 horses.
Third, race the 3 winners left from the first 5 races, and add in 2 second place finishers from the first 5 races. Eliminate the bottom two from that race, and every horse in their group from their first race. You are left with a maximum of 5 horses (possibly less if one of the original first place finishers didn't get in the top 3).
Finally, race the 5 remaining horses to get your overall top 3.
Total of 5+1+1+1 = 8 races.
First, 5 races of 5 horses each. Eliminate the bottom 2 horses of each race. You are left with 15 horses.
Second, race the 5 winners of the first 5 races. Eliminate the bottom 2 of that race and every horse in their group from their first race. You are left with 9 horses.
Third, race the 3 winners left from the first 5 races, and add in 2 second place finishers from the first 5 races. Eliminate the bottom two from that race, and every horse in their group from their first race. You are left with a maximum of 5 horses (possibly less if one of the original first place finishers didn't get in the top 3).
Finally, race the 5 remaining horses to get your overall top 3.
Total of 5+1+1+1 = 8 races.
Race all of them in groups of 5: 5 Races; keep track if which horse was in which race
Race all of the winners: 1 Race; eliminate all the horses from the bottom 2 horses groups including those 2 horses; you have your fastest horse already
Race for second place: 1 race; Race the horse that got second in the previous race against the 4 that the fastest horse beat
Race for third place: 2 Races; Race the third place horse from 2 races ago against the 1st and 2nd places horses
9 total
Race all of the winners: 1 Race; eliminate all the horses from the bottom 2 horses groups including those 2 horses; you have your fastest horse already
Race for second place: 1 race; Race the horse that got second in the previous race against the 4 that the fastest horse beat
Race for third place: 2 Races; Race the third place horse from 2 races ago against the 1st and 2nd places horses
9 total
DrPizza
Administrator Elite Member Goat Whisperer
Another quick solution, if you're looking for a guarantee (edit: I think this actually is the minimum # of races possible, unless some weird if-then strategy yields 6 races)
Start with 5 races. Each horse races in one of these.
obviously, the 4th and 5th place horses from each race are no longer in contention... 10 horses eliminated.
Now for the playoffs.
Top horse from each race in the first playoff
(this is race 6)
whichever horses finish 4th and 5th in that race, you don't have to consider them or the other horses in their first races... you've eliminated a total of 6 more horses... the field has been narrowed to 9.
For the horse that came in 3rd, you don't have to consider the other two horses that haven't been eliminated from its first race
You're down to 7 horses. AND, you don't have to consider the 3rd place finisher of the first race with the horse that came in 2nd; down to 6 horses.
So, what you have left, after 6 races, is
the winner of the 6th race, plus the two horses that finished behind it in the preliminaries
the 2nd place of the 6th race, plus the one horse that finished behind it in the preliminaries,
plus the 3rd place in the 6th race.
You only need one more race to determine the top 3.
Therefore, 7 races total.
Now, to determine the 8th race is a little more tricky..
if from race 1 horses A and B both win, then horse C is potentially faster than the 3rd place horse in the first playoff race... horse C will need to be included in the 8th race. Ditto from race 2, 4, and 5. If the 2nd place horse in the 3rd race places hig
Start with 5 races. Each horse races in one of these.
obviously, the 4th and 5th place horses from each race are no longer in contention... 10 horses eliminated.
Now for the playoffs.
Top horse from each race in the first playoff
(this is race 6)
whichever horses finish 4th and 5th in that race, you don't have to consider them or the other horses in their first races... you've eliminated a total of 6 more horses... the field has been narrowed to 9.
For the horse that came in 3rd, you don't have to consider the other two horses that haven't been eliminated from its first race
You're down to 7 horses. AND, you don't have to consider the 3rd place finisher of the first race with the horse that came in 2nd; down to 6 horses.
So, what you have left, after 6 races, is
the winner of the 6th race, plus the two horses that finished behind it in the preliminaries
the 2nd place of the 6th race, plus the one horse that finished behind it in the preliminaries,
plus the 3rd place in the 6th race.
You only need one more race to determine the top 3.
Therefore, 7 races total.
Now, to determine the 8th race is a little more tricky..
if from race 1 horses A and B both win, then horse C is potentially faster than the 3rd place horse in the first playoff race... horse C will need to be included in the 8th race. Ditto from race 2, 4, and 5. If the 2nd place horse in the 3rd race places hig
chuckywang
Lifer
You got it down to 6 horses with 6 races. How do you determine the top 3 from just one race?
EDIT: BTW, OP. What job were you applying for?
EDIT2: Ok, I see. You don't race the first place horse.
Ok...I'm not reading any of the responses at first, but here is what I think:
Races 1-5
-Produces winners A1, B1, etc. placers A2, B2, etc. and showers A3, B3, etc.
-All 4's and 5's are eliminated
-Still in the running are A1-3, B1-3, C1-3, D1-3, and E1-3
Race 6
-A1 v B1 v C1 v D1 v E1
-A1 win, B1 place, C1 show
-All D and E horses are elminated, C2+ are eliminated, B3+ are eliminated
-A1 is clearly the fastest
-Still in the running are A1-3, B1-2, C1
Race 7
-A2 v A3 v B1 v B2 v C1
-Win and place are 2nd and 3rd fastest...
So...seven races. Is that right?
Races 1-5
-Produces winners A1, B1, etc. placers A2, B2, etc. and showers A3, B3, etc.
-All 4's and 5's are eliminated
-Still in the running are A1-3, B1-3, C1-3, D1-3, and E1-3
Race 6
-A1 v B1 v C1 v D1 v E1
-A1 win, B1 place, C1 show
-All D and E horses are elminated, C2+ are eliminated, B3+ are eliminated
-A1 is clearly the fastest
-Still in the running are A1-3, B1-2, C1
Race 7
-A2 v A3 v B1 v B2 v C1
-Win and place are 2nd and 3rd fastest...
So...seven races. Is that right?
chuckywang
Lifer
You are right. Read my EDITs above.
DrPizza
Administrator Elite Member Goat Whisperer
1st place is already the fastest of the fastest - the winner of the race of the winners. You're down to 6, but know 1st place. That leaves 5 other horses who could get 2nd or 3rd. 7th race, whoever gets first place is the 2nd fastest horse. Whoever gets 2nd place is the 3rd fastest horse.
I didn't fill in that part because I figured if you followed the previous logic, that step was obvious.
chuckywang
Lifer
No, the 2 slowest horses of any race cannot be in the top 3 since there are 3 horses faster than it.
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