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xkcd #3115: Unsolved Physics Problems
(imgs.xkcd.com)
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Bellman's lost in a forest problem: https://en.wikipedia.org/wiki/Bellman%27s_lost-in-a-forest_problem
Generalized moonshine: https://en.wikipedia.org/wiki/Monstrous_moonshine#Generalized_moonshine if the moonshine phenomena also exists outside the monster group
Snake in a box problem: https://en.wikipedia.org/wiki/Snake-in-the-box