Using only combinations of either single or double button presses:
Using 1 press
Using 2 presses
Using 3 presses
Using 4 presses
Using 5 presses
For anyone curious as to my internal process of coming up with these values, I made a quick chart of each type of press combo and how many variations there were for each type, with x indicating it has ...
You have all the possibilities using only single button press
Then the possible combinations using one pair are:
Then you have the possibilities using multiples pairs:
Adding all cases, you get:
Which is the expected answer from the question!
Well, let's see. It's possible for 1 to 5 buttons to be pushed to create a combination, so let's calculate the number of possibilities for each individually, assuming you can pick the order of the buttons to be pushed.
Your lock looks a lot like a Kaba Simplex. This lock allows for codes where the order in which the buttons are pressed matters. Also, it allows for buttons needing to be pressed in unison, or not at all. Each button can be pressed only once, though.
Going by this assumption, we have:
325 Single Buttons Codes
Let's start by just pressing a single button at ...
If you are allowed to press every button one by one only, the answer will be;
which includes non pressing any button to unlock as well. But it seems
You are allowed to press two buttons or more at the same time with one finger.
But after this point this requires a computer programming in my opinion so I wrote a simple program which calculates all ...