# Smallest number of combinations...?

• Jan 25th 2009, 06:51 PM
Saibot
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:

• Jan 25th 2009, 11:11 PM
Constatine11
Quote:

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 $\displaystyle N \ge 1500$.