Thread: Permutation Problem

Hi, my name is Robert and I was just curious about how to figure out how many tries it would take to unlock my new combination lock. The lock has a button in the middle that you press up, down, right or left. You have four directions to choose from. I set the lock to unlock with the input of seven directions. These directions have to be entered in the right order. I was wondering how many tries it would take to unlock the padlock. What kind of formula would be used? Basically, I just find this sort of stuff interesting and I have been out of school for years. Any help to satisfy my curiosity would be appreciated.

I think the answer is (4)(4)(4)(4)(4)(4)(4)=16,384 or 4 to the seventh power. It would take up to 16,384 tries to open the padlock if one knew they needed seven inputs. But, if they didn't know this, they would have to try (4)(1)+(4^2)+(4^3)+(4^4)+(4^5)+(4^6)+(4^7)=? I think there may be an easier way to express this with the explanation mark. Is this correct?

I've been looking at some of the problems on this forum. Some of them make me smile at how darn complicated they seem. I've only had math up to algebra II/Trig and that was 20 years ago. I admire your talents and wish I could speak the language.