Thoughts in bird poop white,
It's a two step process, not only are the other dim guys laughing, but they're also not stopping right away.
Combinations:
1 with 2 without - two laugh, one doesn't. Obvious all around.
2 with, 1 without - all three laugh at first. then, one of the ones with realize that since he's looking at one with and one without, the one with shouldn't be laughing and stops.
3 with - all three laugh. after a while, the bright one realizes that if this were the 2w1wo case (with him obviously being the wo, he knows the other two), then the one or both of the other two should, despite their relative dimness, have cracked this by now and stopped laughing. Knowing that the other two, while able to figure out the simpler case, wouldn't be able to see through this more complex case, he stops.
The trick here is that the question is written in such a way that it's easy to see "laughing/not laughing" vs "clean/dirty" as the only parameter. In fact there are two more, the "keep laughing after a while/stopping" and a scale of the resoning capacity of the participants. The second is vital here, if these were totally random people there might be a posibillity that neither of them crack even the first part, hence laughing at each other indefinitly blissfully ignorant of their own situation or even that one or both of them don't see the humor in the first place. It's assumed that all involved have a degree of knowledge about how the others will and won't act. The solution is based on comparing how long it would these two take to grasp the 2w2wo situation to how long they are actually taking to do it. If they seem to take a long time or even not at all even though they ought, it may be resonable to assume this is actually the 3w scenario and you ought to quit laughing.
