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Riddles

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My solution: Light Josh's pants on fire with the lantern. Josh, more concerned about his pants being on fire than falling, will run like a madman to the other side of the bridge, assuming you pointed him in the right direction. The flame from the pants will illuminate the bridge as he runs, so both he and the rest of the group will be able to see any potential hazards. If he falls, then you can easily manage to get the remaining group members across within the allotted time. If he complains about being selected, you can easily point out that he was chosen in order to maximize efficiency, and that it could be considered a Pigouvian externality tax on his nincompoopery.
This is quite tough but... your 3rd point about the bridge carrying only 1 or 2 people, carrying 1 person at a time would be a bit daft, wouldn't it? I mean, it's not the most efficient way and the lantern would not be able to go back by itself...

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