An XP lamp (tier 6) is an item obtained during the Broken Home quest. It is the sixth lamp obtained in the quest, located in a chest found below the basement, in the room that the player arrives in after using the mountaineering gear to descend the pit. It cannot be obtained on the first playthrough, and requires at least level 60 in each skill. Unlike other items, it can be taken out of the mansion. However, it cannot be banked. Rubbing it gives 32,000 XP in a skill of your choice.
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