Once someone brought up this thread, I disagree with I can only try’s solution to frummy in the tummy’s riddle about the three guys and Bin Laden. In I can only try’s solution, the one who figured out which color hat he was wearing did so by making presumptions about what the other two guys would be thinking. Now these presumptions were on the fact perfectly logical. So why didn’t the other two guys figure it out too? Well there are two possibilities:
1) They lacked the capabilities of logical reasoning.
2) They would have in fact figured it out; they were just slower than the third guy, and the deal was that only the first guy to figure it out gets to live.
The problem is that either of these two possibilities render the third guy’s thought process invalid. His response was based in the fact that neither of the other two guys had figured out that they were wearing black hats. Well if they lacked the capabilities of logical reasoning, or were slower than the third guy, then the fact that they didn’t figure out that they were wearing black hats doesn’t prove anything.
Now it could be that frummy in the tummy was trying to preempt my point when he said:
It could have been Huey or Dewey who figured it out as well, but Louie happened to be faster today.
But it doesn’t really preempt it because it’s basically the same as my second possibility – if they weren’t so quick on that day, (then in the hypothetical scenario where the third guy had a black hat) they might not yet have figured out that they were wearing red hats.
In other words, none of them should ever be able to figure out what color hats they are wearing because they only gauge they have of the speed of each other’s thought process is how quickly they figure out which color hat they are wearing, by which time the game is over.