# Thread: 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 $\displaystyle n$ positions the number of unique combinantions is:

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

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

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