11/1    So for the hallway problem, I get:
           sqrt((x^(1/3)y^(2/3) + x)^2 + (x^(2/3)y^(1/3) + y)^2)
        I might have made a mistake in my calculations somewhere, but
        the calculus looks so ugly that I doubt it's anything simple like
        (x + y)sqrt(2) like someone else guessed.
        \_ Now that I think about it, I'm more confident in this answer.
           If x = y, it simplifies down to 2x*sqrt(2), which is what one
           would expect.
                 \- that is correct, but my formula is nicer. the calculus
                    looks like high school calculus ... although i used a
                    computer to do some of the grunt math. but it's not like
                    you need to use the airy function or anything like that.
                    \_ The calculus is easy; it's just taking a derivative
                       to find extrema.  The algebra just makes it ugly,
                       though.
        \- i used maple to do some of the math quickly ... max len is
           [X^(2/3) + Y(2^3)]^3/2, with reasonable assumptions.
           Solution avail at: link:csua.org/u/9rg --danh
           Harder problems is: unit board/plank vertically flush against a
           veritcal wall. bottom begins to slide away ... at what point
           does the tip lose contact with the wall. [from klepner and
           kolenkow].
        \_ the problem is ill-stated.  we need to know the height of
           the halls as well (as anyone who has actually moved a large
           object up an interior stairway and landing would tell you).
           \- obviously the question is being asked in 2-d with a zero
              width rigid board.

[ MARS, bitch. ]
\_ I'm Rick James, bitch.
\_ I'm rich, bitch.
\_ I'm dead, bitch.
\_ What, me dead?  -Alfred E. Neuman
              \_  That's not obvious at all.  Anyone care to solve the
                  3d case?  I'm reminded of the sofa simulation in Dirk Gently's
                  Holistic Detective Agency.
                  \_ figure out how far you can tilt the board, finds its
                     dot product with the floor, and then solve the 2D case
                     for the effective length.  assuming the height is
                     not changing around the corner and the floor/wall/
                     ceiling interfaces are all right angles.