You have been charged with finding the 3 fastest horses out of a group of 25. You also need to know which is first, second, and third. You know that any given horse always finishes a race in exactly the same amount of time. You also know that the horses' times are unique (i.e., no two horses ever tie.) You have a racetrack in which you can race up to 5 horses per race. The problem: You are charged 25 dollars per race, and you do not have a stopwatch. You are only able to record the relative positions for each race. (Which horse came in first, second, third, fourth, or fifth?) Find an arrangement of races in which the cost out of your pocket is minimized, and where you always succeed in finding the first, second, and third fastest horses