Practice Permutations Problem


Let’s say you have a combination lock with the numbers 1-60 on the dial, and the combination consists of 3 numbers.

Suppose consecutive numbers in the combination must be at least 5 apart (e.g. if the first number is 17, the second number can’t be in the range 13-21). If your number is near 1 or 60 you can’t be within 5 when “wrapping around” either (e.g. if the first number is 58, the second number can’t be in the range 54-60 nor 1-2). 

Question 1

How many combinations are possible with this restriction?

Question 2

If you have a school of 1200 students, how many numbers would the dial on the locks have to have to make it possible for each student to have a lock with a unique combination?

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s