You want to find out the fastest 3 horses among 25. You can race at most 5
at a time to find out their relative speeds. How many races are required to get the top 3
horses?
7 races:
First run races in unique groups of 5. The last two in each group are thus immediately eliminated. Second, run a race of the 5 winners. The winner here is the fastest horse. The slowest two in that race are also eliminated, as well as all of those that previously raced with the slowest two in their group of 5 races.
In the groups of 5 races, those that raced _behind_ the 3rd placer in the race of winners are eliminated. Likewise the third horse in the original group of 5 behind the 2nd placer in the race of winners is eliminated.
The 1st placer and the remaining contenders are shown below as a 1 and 0s respectively in their order in the original groups of 5 with the rows sorted by how the lead horse placed in the race of winners. All X's have been eliminated as explained above.
XX001
XXX00
XXXX0
XXXXX
XXXXX
Race as the 7th race the 5 0's. The best two will the 2nd and 3rd fastest horses.
Edited on August 1, 2019, 11:30 am
soln
