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Math Help - Smallest number of combinations...?

  1. #1
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    Smallest number of combinations...?

    There are 1500 students in a high schoole. Each student requires a lock for a personal locker/ The school provides locks.

    The locks work so that they have 3 consecutive positions to hit before it opens. Each consecutive position must be different from the one previous (therefore there are 60*59*59 possibilities).

    What is the smalleset number of positions that must be in the lock to give each student a unique combination?

    I have the answer, i just dont know the method for getitng it:

    Answer: 12 positions.
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  2. #2
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    Quote Originally Posted by Saibot View Post
    There are 1500 students in a high schoole. Each student requires a lock for a personal locker/ The school provides locks.

    The locks work so that they have 3 consecutive positions to hit before it opens. Each consecutive position must be different from the one previous (therefore there are 60*59*59 possibilities).

    What is the smalleset number of positions that must be in the lock to give each student a unique combination?

    I have the answer, i just dont know the method for getitng it:

    Answer: 12 positions.
    If there are n positions the number of unique combinantions is:

    N=n \times (n-1) \times (n-1)

    Now make a table of N against n, you want the smallest n such that N \ge 1500.

    .
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