Quote:
Originally Posted by pdurrant
First, split the horses into five groups of five, call them A,B.C.D & E groups. Race each group. Call the fastest horse in each group A1, B1, C1, D1, E1; the second fastest horse A2, etc.
Take the top three horses from each group - 15 horses in all. The fastest three horses of the 25 must be in this fifteen.
Split the fifteen horses into three groups:
Alpha Group: A1,B1,C1,D1,E1;
Beta Group: A2, B2, C2, D2, E2;
Gamma Group: A3, B3, C3, D3, E3
Race each group.
The fastest horse of all is the winner of the Alpha group.
The second fastest horse is either the horse who came second in the alpha group, or the horse that came first in the beta group
The third fastest horse is either the horse that came second or third in the alpha group, or the horse that came first or second in the beta group, or the winner of the gamma group.
That is, the second and third fastest horses are two out of five horses. Run those five horses in a race, and the first and second of that race are the second and third fastest overall.
Total number of races required: 5+3+1 = 8.
(The trick is to realise that after the second lot of races, we can already see who the fastest horse is.)
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You need 6 races to determine who is first as per Paul's logic above. Then you just need 1 more race to determine the second and third place horses, running the horses Paul has listed above to determine third place.
So Paul's logic is correct, he just added up the races incorrectly. And 5+3+1 != 8.
Actually, I see where Paul got 3 now. So my answer seems to be wrong, logic-wise, although it's probably correct from Hamlet's hint.
Anyway, 5+3+1 still doesn't equal 8.