New month, new questions. I have already posted all my geometrical questions. This month, I have numerical and combinatorial questions for you.
2.01 In a sport contest lasting n days (with n > 1), m medals are awarded. On the first day, one medal and 1/5 of the remaining m-1 medals are awarded; on the second day, two medals and 1/5 of the then remaining medals are awarded; and so on. On the last day, the remaining n medals are awarded. How many days does the contest last and how many medals are awarded altogether?
2.02 Five students, A,B,C,D, and E take part in a contest. One prediction was that the contestants would finish in the order ABCDE. In fact no contestant finishes in the position predicted, and no two contestants predicted to finish consecutively actually do so. A second prediction had the contestants finishing in the order DAECB. This prediction was better: Exactly two of the contestants finish in the places predicted, and two disjoint pairs of students predicted to finish consecutively actually do so. Determine the order in which the contestants finish.
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