squarehead11

3D printer manufacturer Bambu Lab has released an update for their X-family of printers. The change introduces the requirement to "authenticate" requests to their printers API, breaking third-party software integrations. To control a printer remotely, users are now required to use the new "Bambu Connect" software, an electron app in beta state.

Shortly after the release, some people have already reverse engineered the software and extracted the "private" access key, which appears to be hardcoded within the app: https://wiki.rossmanngroup.com/wiki/Reverse_Engineering_Bamb...

I believe it would be 7290, or more generalized, S(N) = 10 * 9 ^(N-1) with N being the length of the code and S being the number of combinations (assuming that a decimal system is used)

And from there, with variable lengths ranging from L to H, S(L, H) = 5/4 * 9 ^(L-1) * (9^(U-L+1) - 1)

So if the bank allows combinations from 4 - 6 digits, there would be a total of 663390 combinations to choose from.

Now, of course, the bank may decide to go from decimal to hexadecimal in the future - or maybe, there systems allow only duodecimal. In any case, the formula can be generalized further to account for all number systems - with B being the base of the system:

S(L, H, B) = (B/(B-2)) * (B-1) ^(L-1) * ((B-1)^(U-L+1) - 1)

This is only defined for B > 2 - in binary system, there's only ever two combinations which fit the constraint