Proposed by Stephen Morris, Newbury, U. K., and Stan Wagon, Macalester College,

Question

Proposed by Stephen Morris, Newbury, U. K., and Stan Wagon, Macalester College, St. Paul, MN. You are organizing a racing event with 25 horses on a track that can accommodate five horses per race. Each horse always runs the course in the same time, the 25 times are distinct, and you cannot use a stopwatch. Show how to arrange 7 races so that after all races are run, you will have enough information to determine which of the 25 horses present is fastest, which is next fastest, and which is third fastest. You may use the results of earlier races to schedule which horses compete in later races. Show that with just 6 races, it is not possible to be sure of knowing which are the top two horses. Give a procedure that uses 6 races and, with probability at least 3/10, yields information sufficient to determine the fastest horse and the runner up. You have no a priori knowledge of the relative strengths of the 25 horses. Give a procedure that uses 6 races and, with probability at least 1/20, yields information sufficient to determine which horse of the 25 is fastest, next fastest, and third fastest.

Explanation / Answer

where is question ???

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.