As Gandalf said, it would take weeks and weeks of trekking out of their way to go around Mirkwood. Hundreds of miles out of their way. It would be much too bothersome and time-consuming, rather than just cutting straight through it.
It was too long of a trip and it would have taken them past Dol Guldur to the south and orcs or dragons to the north.
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Gandalf tells Beorn the story of the journey from the start to the point that takes them to Beorn's house. Beorn is intrigued and entertained and so, as the group are no threat to him, he allows them to to stay in his house for the night. While they sleep, Beorn travels to discover if the tale he has been told is true. It is and as they have killed the Great Goblin (Beorn hates goblins) he agrees to give the group supplies and ponies to take them to Mirkwood.
Who suggest Ralph & Piggy should go to the party in Chap.9
Sarah Ellen
It is a royalty free song called Party Hard.
I would look in your local listings or go to a party store to get some details.