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?

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