A challenge for all
Oh stop it you guys. 
There, are you satisfied?
It's amazing how one little comment (my grammar lesson) can side-track a thread so easily.
Could you turn that into an instance for me as I am having a little trouble figuring out how to get it work as an instance?
Yes I did. (FYI: It is "see the..." not "saw the..." since you are in essence asking a question which begins with "Did you...". Just letting you know.)
I took "protoborg:" as the subject, or an implied "you," which wouldn't require a form of "to do" with it. English is such a strange language.
Well, regardless, you still need a form of "to do" because "you saw the...?" is lazy. "Protoborg saw the...?" is bad grammar.
Also, the sentence was direct at me directly. Therefor, it was meant as a direct question which means it requires the "to do" form of the word. In other words, she said "Protoborg, saw the...?" No one would ever say that in person. They would say "Protoborg, did you see...?" or "Protoborg, you see...?" The thing is it is more likely they would ask the first way as the second is rather awkward. Actually, most people would probably say "Protoborg, ya see...?" since the average person in this country is remarkably lazy. 
Also, the sentence was direct at me directly. Therefor, it was meant as a direct question which means it requires the "to do" form of the word. In other words, she said "Protoborg, saw the...?" No one would ever say that in person. They would say "Protoborg, did you see...?" or "Protoborg, you see...?" The thing is it is more likely they would ask the first way as the second is rather awkward. Actually, most people would probably say "Protoborg, ya see...?" since the average person in this country is remarkably lazy.
True. I'm suddenly reminded of Shaw's preface to Pygmalion. 
Anyway, if you want my solution, you just need a bunch of logic_branches which you can ToggleTest for each button. Then set certain outputs of OnTrue and OnFalse to add to a counter. When it hits 8 all of the bits are correct, and the Enter button can trigger a relay that the counter enables/disables.
Anyway, if you want my solution, you just need a bunch of logic_branches which you can ToggleTest for each button. Then set certain outputs of OnTrue and OnFalse to add to a counter. When it hits 8 all of the bits are correct, and the Enter button can trigger a relay that the counter enables/disables.
That could work. It seems rather more unwieldy than Lp's solution, though. Her solution does use a counter in a similar fashion, however, so what do I know. 
I haven't looked at hers, but you could probably make an instance of it just by copy-pasting from the posted VMF. Without my Windows box I can't look at the file, though, so I could be completely wrong.
My solution is rather simple:
0) create two math_counters, the master counter and the end counter.
1) Get the binary numbers that represent the letters.
2) Convert the binary numbers to decimal numbers:
P 01010000 80
R 01010010 82
O 01001111 79
T 01010100 84
O 01001111 79
B 01000010 66
O 01001111 79
R 01010010 82
G 01000111 71
3) Get eight buttons
4) button 1: add 1 to the counter; that's the last number
5) button 2: add 2 to the counter; that's the second last number
6) button 3: add 4 to the counter; that's the third last number
7) button 4: add 8 same for button 5,6,7,8
Create a logic_compare for each number you want to have an output for and give them all the same name.
9) let the master counter compare the logic_compare (s) compare as soon as its value changes. So every time a number changes it's checked against all the logic compares.
10) give the logic compares outputs:
- let the logic_compares kill themselves when they meet the requirement;
- let the logic_compares add 1 to the end counter for the number of correct letters
11) give the math_counter a onhitmax output, you solved the puzzle.
To make it visible for the player you could make a material that has all letters as a texture index; so it is visible for players what is happening
I could've probably done it somewhat simpler but this works!
Nice! You could also use the end counter to enable/disable the logic_compares through a logic_case: when it changes it disables them all, then the case enables the correct one.