Thread: 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.

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:

Answer: 12 positions.

If there are positions the number of unique combinantions is:



Now make a table of against , you want the smallest such that .

.