Cracking a Safe with UX

Your mission, should you choose to accept it, is to figure out the four-digit code of this safe with just one try:

With only four keys being schmutzed we know whoever punches in the code touches only 2, 5, 8 and probably 9. With four options we have just 256 codes to try.
However, since it's pretty obvious that digits aren't repeated in the code (otherwise we would not see as many as four dirty buttons), the number of combinations drops to just 24. 

But can we use our UX expertise to crack this code in less than 24 tries (at most)?

First, the rules should be made clear. In this keypad you have to first press the key button, then the four-digit code, and then the key button again. Now let's have a crack at it.

Which digit is first? That's actually really easy to guess using Fitts' law.

Fitts' law is about ergonomics - how people use machines. Specifically it's about pointing. What it says sounds almost trivial: the bigger and closer the target, the easier it is for us to point to it accurately. So if a button is bigger, it's easier for us to point to it. The same goes if a button is closer to our finger - the farther it is, the less accurate we are at pointing to it.

We can deduce from Fitts' law that the larger the dirt circle around a button, the more the finger had to travel to get to it. The button with the biggest circle of dirt is clearly 2. This means the finger that presses 2 travels the farthest distance from its initial location. Because the distance is so great the finger usually misses it quite a lot, hence the large dirt circle. So its likely that 2 is the first button pressed. The finger has to start from the key button, then travel the greatest distance to 2, and then continue to some other key. 

Great. 

Code thus far: 2 _ _ _

We're down to 6 possible combinations. But can we narrow it down even more?

Which button is next? If 8 were the second digit, followed by 9 or 5, we would expect to see a bigger dirt circle around 8 than around 5, right? Because the distance from 2 to 8 is greater than from 5 or 9 to 8. Clearly, then, the next key is 5. And now there are just two left.

Code thus far: 2 5 _ _

So which is the 3rd button: 9 or 8? 9 has the smallest dirt circle around it, so it stands to reason that the finger travels a very short distance in order to get to it. This seems to suggest that we need to press 8 and then 9. But if that's the case then why is the circle of dirt around 8 bigger than around 9? Both are pressed after adjacent buttons, after all, so shouldn't we expect them to have the same sized dirt?

Time to think about ergonomics some more. Since the key pad is mounted on a door we need to raise our hand in order to tap on it. Now it's a bit easier to move your finger sideways in this position than up and down. Why? In order to move your finger vertically you have to move your elbow, which requires your shoulder muscles to go to work. Those are some big joints. In contrast, move between horizontally adjacent buttons your elbow can almost stay in place, with only the rest of your arm moving. Try it. I'll wait for you.

See? So vertical moves are harder, and therefor we can expect buttons that are pressed after horizontally adjacent neighbors to have smaller dirt circles than those pressed after vertically adjacent neighbors.

So it's 8 and then 9.

Code: 2 5 8 9

Just one attempt.

Conclusion: Fitts' law works all over the place, not just in computer GUI.

Also: clean your damned keypads.

We used Fitts' law when we designed our new Bubble Menu interface:

The buttons inside the bubble are relatively big and since the bubble opens up wherever you start dragging from the buttons are always close to the mouse's cursor. Close and equidistant. 

So go sign up for Gigantt. Active beta users will enjoy a lifetime discount when Gigantt leaves the beta phase.