saw an interesting problem last night
if there are 25 ducks, and you can only race 5 ducks at a time, how many races do you need to see which 3 ducks are the fastest?
each race will only tell you their relative speeds (ie ducky 3 was the slowest, but ducky 4 was the second fastest)
25 ducks.
Race 5 times, eliminate the 2 slowest from each race. As there's no possibility that they will be in the top three overall if they couldn't be the top three of their own race.
15 ducks.
Race 3 times, again, eliminating the 2 slowest.
9 ducks.
race 2 times, eliminating 2 from the first race, and then including the 3rd place of the first race into the second race, then eliminating the two slowest from that.
5 ducks.
Race them.
11 races