# Math Help - Smallest number of combinations...?

1. ## 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:

2. Originally Posted by Saibot
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:

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 $N \ge 1500$.