[rookie1ja]

Christmas Tree - Back to the Logic Puzzles
Four angels sat on the Christmas tree amidst other ornaments. Two had blue halos and two – 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?

Spoiler for Solution:

Christmas Tree - solution
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).

Spoiler for old wording:

There were 4 angels on a Christmas tree (Edit: and the angels knew that there were 4 of them). Two had a blue aureole and two yellow (Edit: the angels knew that, they just did not know who had which color AND the angels know which angels can see which angels), however none of them can see behind his head. Angel A is on the highest place and he can see angels B and C, which hang below him. Below hangs angel B, who can see only angel C under him. Angel C can't see anybody, because angel D hangs under a twig (nobody can see him and he can not see anyone either).
Which one of them will be the first to guess (Edit: speak his guess out load, deduce and say) what his own aureole is?

[qazqaz]

what about a lucky guess

[Incognitum]

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what about a lucky guess

A lucky guess is to a logic puzzle as a Cuisinart is to a jigsaw puzzle; Yes, it's quicker, and at the end all the pieces fit together nicely, but it's not something you really want to spend your time looking at.

[axmillia]

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what about a lucky guess

A lucky guess is to a logic puzzle as a Cuisinart is to a jigsaw puzzle; Yes, it's quicker, and at the end all the pieces fit together nicely, but it's not something you really want to spend your time looking at.

Nice analogy(sp?).

[anuraag]

If A does not speak out, B will be able to guess that his aureole is he colour other than that of C.

[csharpner]

The wording should be changed to say that the Angels actually speak their guess out loud. I read "guess" as "silently figuring it out" because "guess" is an internal thought process, at which point I concluded that A was the only one with any hope of figuring out his own color and only when B&C have the same colors as each other.

So, when a guess IS possible, it's only A that can do it... unless the wording is changed.

[RMW]

what's the point of D

[twittbrod]

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The wording should be changed to say that the Angels actually speak their guess out loud. I read "guess" as "silently figuring it out" because "guess" is an internal thought process, at which point I concluded that A was the only one with any hope of figuring out his own color and only when B&C have the same colors as each other.

So, when a guess IS possible, it's only A that can do it... unless the wording is changed.

Not to mention that previous posts (and the nature of a logic puzzle) dictate that they're not actually guessing.

[SPENGLER]

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what's the point of D

to be lonely, and to use up the 4th colour allowing A,B,C to be unsure. it would be the same as saying that there are four aureole's, and only 3 angels.

[nhales]

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The wording should be changed to say that the Angels actually speak their guess out loud. I read "guess" as "silently figuring it out" because "guess" is an internal thought process, at which point I concluded that A was the only one with any hope of figuring out his own color and only when B&C have the same colors as each other.

So, when a guess IS possible, it's only A that can do it... unless the wording is changed.

That's exactly what I was thinking. At first I thought that "logically" the only angel with a chance in hell of making a guess was A. I didn't realize they were having a competition to see who came up with the answer first and therefore saying the guess aloud. But then again, I've never had a speaking angel on my tree either.