I have just about no idea what to do.
I solved the problem itself in a minute or two, then I took a big look at the room and sighed.
First of all, (in once south), I tried entering the numbers in binary in the two first reachable binary counters. The binary thingy at the top did, sadly, nothing. I presume it was just for trying out.
Anyways, I quickly found the task of entering my binary solutions, secreted here, impossible.
Click here to view the secret text
×37*7=259.
In binary, that's 000111 times 100101.
When entering the number into the binary counters, the doors always alternate from closed to open, so the two counters' values can only differ by a maximum of 2.
I wrote a quick program to check, and indeed the only possible answer (except of course, 1) is mine, as it's impossible to enter a fractional number.
I tried randomly running around some other doors, and now's I'm totally confused as to the system.
Why are there about 5 different binary counters when only two would suffice?
-Insane