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No, an Xbox 360 game will not run on an original Xbox.
Theres a sonic game for XBOX 360, but I forgot about it for the XBOX
no the xbox can not understand the format of a xbox 360 game (its too new to be used on an xbox)
XBOX Live is not a game console.
It's a online game service for the XBOX 360.
if it is a Normal Xbox game and you want to play it on the xbox you may need to manually update your xbox