Follow the rules listed below to determine the GA code, All rules are numbered.

1. The GA code consists of α characters.
2. The arithmetic solution to (2α-β) is a Prime Number
3. There is only one NUMBER in GA code.
4. The alphabetic position of the 4th character in the GA code is 4 letters after the character in the code's 2nd position.
5. Last letter in GA code is upper case.
6. The first three letters of the GA code are the same case.
7. The rule two rules before this one is false.
8. The NUMBER in GA code is the first or last character in GA code.
9. One of the characters is either first or last letter in the English alphabet.
10. The character mentioned above is not the final letter of GA code.
11. The NUMBER in GA code is not a Prime Number.
12. The alphabetic position of the character in the 2nd position of the GA code is the The arithmetic solution of ([It's position] + [NUMBER from GA code]) (i.e. n'th letter of alphabet.)
13. Not all letters are the same case.
14. Letter in 4th position of the GA code looks similar to a number and is often confused with it in GA codes.
15. The alphabetic position of the last character from the GA code, which is a single-digit number, and the NUMBER from GA code are two different numbers yet both are evenly divisible by the same number β=/=1 (without remainder).
16. The arithmetic solution to (α+β) is NOT the NUMBER from GA code, and the number of rules in this puzzle divided by 4 is also NOT the NUMBER from GA code.

PS. There is no hidden reason behind bolding some NUMBER words. Sometimes i use number to talk about numbers themselves and sometimes I talk about one specific NUMBER so made it this way just to make things easier for you guys ;)

PPS. If you have questions, find a bug or anything, want to beg for hints (not that I'm gonna give you any;p) - post comments in this topic not in main GA topic. If all people start posting about all 2X puzzles in main topic it will become unreadable ;)

PPPS: I'm an idiot, forgot to add link to event topic ;p

MORE PUZZLES AND AWESOME REWARDS AT MARCH PUZZLE EVENT TOPIC

SOLUTION:

Solution to Logic - Reasoning:
GA code you were looking for was http://www.steamgifts.com/giveaway/9KZOf/blackguards . Only 4 GA codes meet all rules set in Entry GA. 9K[AZ]O[cf] so you had only a total of 4 codes to check: 9KAOc, 9KAOf, 9KZOc and 9KZOf.
There were multiple ways and routes to get solution plus some rules were totally not necessary and only there to let you check with multiple sources if what you got is right. You can see a lot of discussion over the puzzle and solutions in Blackguards GA linked above, so below I will just present you one of possible solutions.

1. From #3 we know there is only one NUMBER in GA code.
2. Rule #8 tells us NUMBER is either 1st or last character of GA code.
3. Rule #15 says about alphabetic position of last character in GA code mreaning it must be alphabet letter and it cannot be number, thus NUMBER must be 1st character of GA code and 4 next characters are letters.
4. Rule #13 tells us that not all letters are the case mase, aka we have lower and upper case letters in GA code.
5. Rules #5+#7 tell us that last letter in GA code (and we already know it will be on 5th position) must be lower case.
6. Rule #6 tells us that 1st three etters must be the same case. since we know there are both lower and upper case letters in GA code and 5th character is lower case it means letters on positions 2,3,4 bust all be upper case.
7. From #14 we learn that 4th letter is often confused with number in GA codes. We can think of several letters like that - O confused with 0, l (lower case L), I (capital i) both confused with 1, b confused with 6.
8. So it cannot be l (lower case L) or b, because they are lower case. 4th character can be O or I (upper case i).
9. I is 9th letter of alphabet, O is 15th.
10. From #4 we can find possible corresponding letters for 2nd position in GA. I->D or O->K.
11. Using #12 we check these letters. for D it would mean that 4=2+NUMBER, NUMBER would be 2, and as #11 tells us NUMBER is not Prime it cannot be 2. So it must be O, K combination.
12. Using #12 again knowing it's K we get 11=2+NUMBER. So we know the NUMBER is 9.
13. From #15 we get that alphabetic position of last letter is a single-digit number (1,2,3,4,5,6,7,8,9), and NUMBER (9) are two different numbers divisible by the same number β=/=1 (without remainder). We can divide 9 without remainder by 1, 3 and 9. β=/=1 and these are 2 dfifferent numbers, so β=3. What other numbers 1-8 are divisible by 3? Only 3 qand 6. aka last letter in GA code is either 3rd or 6th letter of alphabet, so it's c or f.
14. Let us look on our GA code now: 9K?O[cf].
15. Rule #9 tell us that one of the letters is either first or last letter in alphabet, so a or z. We don't have a nor z in GA code yet so it must be on 3rd position. We also know it must be upper case. This way we ended up with GA code 9K[AZ]O[cf] which gives us only 4 possible solutions and which we can easilly bruteforce :>