TL by CrowKarasu

大神翻一下吧。。。

Base +4, StanTC +3, dudumeng +6, asdid +1, halfwise +6

Right, it's clear that all three gags are pink, because if one slave's, yours, was green, the other two wouldn't immediately be sure what color theirs was, until they noticed the slave with the pink gag wasn't immediately released, so they'd know they had a pink one.

Base +8, dobuch +7, ranoya +6, akoss +6, Knight of Blue +6, Slobber +30, mellowjello +8, BakaChibi +6, HeavHo +9, 151132 +7, vfjTgw +14, ssgja +6, T@L +6, and 4 more...

@d3112: Nope, it has nothing to do with the others not being released.
The reason is simple:'
Since it is a "game" they all must have a chance to be released.
But with the two given conditions anyone who has a green gag would not have any chance to be released to begin with.
Hence everyone must have a pink gag otherwise it would not be a "game" for that "participant" at all.
The smartest girl just realized that the game is about noticing this fact and therefore knew her gag was pink.

Base +7, akoss -6, Knight of Blue -6, tictac401 -6, RaPiDJazZ +6, joseph_864 -6, glabr +6, 8XFP -6

@talh I believe @d3112 has the correct answer

Base +6, HeavHo +9, Knight of Blue -6

Thanks for the translation!

Base +7, Arpatron +6

more patchouli doujin is what i live for.

Base +6

This ticks so many boxes for me:
-slime
-living clothes
-orcs

Base +6, Bob64 +7

Just to break the puzzle down so people can understand. The rules states this. If you can confirm that two other gags are green, you're free to go (You see two green, you 'voice out' and you can go). If you can confirm that yours is Pink, you're free to go. Now in the situation given, all 3 are Pink. This means Condition 1 can no longer allow either of them to escape, leaving only the possibility of Condition 2. Let's step into the shoes of Slave 1.

Going by Elimination of 3 possible scenario's (3 Green would mean everyone would 'voice out' leaving only 2 Green 1 Pink or 1 Green 2 Pink and 3 Pink), if Slave 1 saw Slave 2 and 3 with Pink, she may assume that she has a Green Gag giving us a 1 Green 2 Pink. If this is true, Slave 2 and 3 will see a Green and Pink each.

This leaves the possibility where Slave 2/3 might think they have a Green Gag making it 2 Green and 1 Pink, however, this fulfills Condition 1 and the Slave with the Pink Gag would easily point it out and be free, leaving the two Green behind. Since nobody said anything, this Possibility is removed. Thus 2 Green and 1 Pink is not possible leaving either 1 Green 2 Pink or 3 Pink.

Now we backtrack one step up, where we have 1 Green 2 Pink. Let's say Slave 1 has Green and Slave 2/3 have Pink. Now remember that if there were 2 Green, the Pink gets to be released? If Slave 2 thought she had a Green Gag as well, Slave 3 should have just escaped as she would seen 2 Green as Slave 2 can confirm that there is another Green. Since she did not, it means Slave 2's Gag is not Green making it Pink by elimination and she can escape. Thus, 1 Green and 2 Pink is solved.

Coming down to the real scenario, 3 Pink. Why did I have to prove all of the above? Remember I proved that if there were 1 Green and 2 Pink you can determine if you were Pink? Now the fact that Slave 2/3 did not escape, means that they also see 2 Pink. This means that yours and the other person both have Pink Gags. Which proves that your Gag is Pink as any Green would have allowed someone to escape.

Base +6, RefinedFapper +6, Resko +7, glabr -6, MyDesiredDisplayN4m3 +4, tictac401 +6, Noneofyourbusiness0 +6, The Inker +8, illumini9 +6, Saa-Chikou +9, shutupanddrive +6, RubyRoy +4

Unfortunately the puzzle depends on how fast people think.
@annonnymous correctly points out that the slaves can deduce when they are pink both from the possibility of 2P1G and from 3P.
Deducing pink from 3P only becomes viable when enough time has passed to eliminate a quicker deduction from the 2P1G scenario.
That's similar to how the 2P1G deduction only comes after 1P2G can be eliminated (which should be an instant deduction).

The puzzle needs to be modified so that the amount of time given to think is standardized.
Perhaps slaves see each other but are not allowed to see who has been able to escape until the next day.
After 3 days they'd all be able to escape. That's assuming that they are all perfectly logical and know each other to be logical.

Base +6, Resko +7, Saa-Chikou +9

So, Patchy pretty much made a hentai version of Touhou Labyrinth and got herself trapped in it...

Nice!

Base +7, Jellyfish Cannon +10, Prof. Tree +7

ast4 is right. Even if a slave figures the puzzle out, she doesn't know whether the other two have, and it's necessary for them to all do so before the 3P vs 2P 1G can be solved.

Base +6