The Power Of Math Unlocks Many Doors

In the mid-1980s, I worked for a naval architecture firm. Our building didn’t have a secure entrance; you could just call an elevator from the garage or walk in the front lobby door at any time. Our office suite, however, did have a mechanical cipher lock. It had five buttons, and the office manager regularly reset it to a three-digit code for security purposes. Due to the mechanics of it, duplicate digits weren’t possible for an entry code.

One Saturday, I went in to finish some work because I’d left early on Friday. But when I got to the suite, the code that had worked Friday didn’t work today. I really needed to finish my work, and I didn’t think anyone else would be in the suite, so knocking wouldn’t help. This was before cell phones, so I couldn’t call anyone. Even if I’d had a cell phone, I knew only one coworker’s number, our receptionist.

I went down to our lobby, which had a payphone, and called her apartment. There was no answer. I then started thinking about the cipher lock. With only five possible digits, and using only three uniquely, there were only sixty permutations possible. So, I went up to the suite and started trying all the permutations: 1-2-3, 1-2-4, 1-2-5, 1-3-2, 1-3-4, etc. In less than a minute, I’d hit upon the new code. I went in and finished my work.

On Monday, I went to my office manager and told her how easy it was to crack the cipher lock. She then looked at the lock manual and decided to incorporate simultaneous button presses to make it more secure. I then noticed that we had a new receptionist. The office manager said our previous receptionist had been fired late Friday, and that’s why the door code had been changed.

It was a good thing, then, that she didn’t answer her phone. That would’ve been an awkward conversation.