The answer
The answer to the questions shows
that it depends on the shape of the tree and the probability that
a monkey is a liar. After a little thinking this is nearly
obvious.
I can answer the question if all monkes act in the same way, i.e.
they all lie all with the same probability. If this probability
is bigger than a critical value, then it is not
possible to construct the message in the root from the patterns
of "YES!" and "NO!" in the top of the tree.
If the lying probability for the monkeys is bigger than this
critical value it is impossible to reconstruct the Signal from
the racoon at the root.
This critical value depends just on the shape of the tree
- more precisely from the average number of branches
- the branching number.
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