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But still, why 3? why not 4 or 5 or 6?
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Because it could be done in three.
It is optional to set a maximum number of links. But, if the question-setter sets a maximum then it must be done in that number. Otherwise it can be done in up to 6 degrees (hence the name of the game).
But you used Sauron anyway, Perky.
How about
:
Ghân-buri-Ghân -> Merry -> Glorfindel -> Ecthelion -> Gothmog.