permutations

#1
1. A combination lock has 60 different positions. To open the lock, you move to a certain number in a clockwise direction, then to a number in the counterclockwise direction, and finally to a third number in the clockwise directio. If consecutive numbers in the combination cannot be the same, how many different combinations are there?

for this question i got the answer 60*59*59

2) There are 1500 students in Hall C.S.S. Each student requires a lock for a personal locker. The school provides a standard brand of lock for all students. If the locks are to operate the same way as those described in question 1, what is the smallest number of positions that must be in the lock to give each student a unique combination?

if anyone can help me that'll be great :)
 

JohnM

TS Contributor
#3
Your answer to #1 is correct. Beginning with the first number, there are 60 possibilities. In the second number, there are 59 left. In the third number, there are also 59 left, since we can repeat the first number (first and third aren't consecutive).

In the second number, we use the pattern from #1: n*(n-1)*(n-1) and it states that we need at least 1500 unique combinations, so we start with:

n*(n-1)*(n-1) >= 1500

Start with some small numbers for n, plug in and compute, and keep going until we barely exceed 1500.

Example - if we start with n=7, then we have 7*6*6 = 252, which isn't high enough - keep going up until your answer is >= 1500.