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    $\begingroup$ Actually, each failed attempt removes 2 doors and divides the rest in 2, rounded to the nearest odd number. The number of possible doors goes like this: 2001 -> 999 -> 499 -> 249 -> 123 -> 61 -> 29 -> 13 -> 5 -> 1. So, in the worst case, you have 9 failed attemps. The 10th attempt is guaranteed to lead you to freedom. You are free in 9.5 hours or less. PS: plus maybe half an hour to walk between the doors between attemps. $\endgroup$
    – Florian F
    Commented May 27, 2020 at 7:22
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    $\begingroup$ @FlorianF you need to add the time spent walking east and west. $\endgroup$
    – msh210
    Commented May 27, 2020 at 7:24
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    $\begingroup$ @musefan doesn't matter as long as you remembered which hallway you are on right now. $\endgroup$
    – athin
    Commented May 27, 2020 at 13:24
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    $\begingroup$ @athin: Doesn't matter?? My brain disagrees. I would probably lean towards the other path as I would feel bad the one path got visited twice and the other didn't get any visits. I wouldn't want the odd path to make fun of the even path for never getting used. Perhaps I am overthinking it... $\endgroup$
    – musefan
    Commented May 27, 2020 at 13:49
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    $\begingroup$ You should return via the other path, because what if you find a nickel on the floor? $\endgroup$
    – Tanner Swett
    Commented May 27, 2020 at 14:50