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).
How many combinations are possible with this restriction?
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?