Four angels sat on the Christmas tree amidst other ornaments.
Two had blue halos and two had yellow.
However, none of them could see above his head. Angel A sat on the top branch and could see the angels B and C, who sat below him. Angel B, could see angel C who sat on the lower branch. And angel D stood at the base of the tree obscured from view by a thicket of branches, so no one could see him and he could not see anyone either.
Which one of them could be the first to guess the color of his halo and speak it out loud for all other angels to hear?
December 25th, 2014 | Category: 
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Angel A, for he could eliminate the color of the other angel halos and have a high likelihood (50%>) of guessing correctly.
…there’s almost certainly something I’m not seeing here.
Though really, any of the angels could GUESS their halo color–though not accurately. It’s a matter of timing.
Angel A could easily say what color his or her halo is only IF B and C’s halos are the same color, but if they are not, then it could only be angel B who would realize his or her halo is the opposite of the one he can see (angel C).
In other words, if Angel B and C’s halos are the same color, then Angel A can immediately announce the color of his halo (because it can’t be the same color as the two he can see). BUT . . . if Angel A says nothing, then Angel B knows his halo is NOT the same color as Angel C’s (because if it were, Angel A would have said something). Curiously, in this situation, Angel C would eventually be able to deduce for certain what color his or her halo was, but A & D would remain in the dark. Whereas in the first scenario (where B and C have same color halos), all the angels would eventually know their halo color. Angel A would announce first, then B would know, too. Lastly, C and D would know at the same time. It’s a fascinating riddle because the uncertainty of Angel A is what makes it possible for Angel B to be certain. Who knows what other things in life we COULD be aware of if we were smart enough to infer them from others’ unknowing?
Taylor you have it in there.
There are 2 possible solutions: 1. if angels B and C had aureole of the same color, then angel A must have immediately said his own color (other then theirs), 2. if angels B and C had different colors, then angel A must have been silent and that would have been a signal for angel B, who could know (looking at angel C) what his own color is (the other one then C had).