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Tsk-tsk, semantics again (the bane of logicians)
09/03/2019, 16:14:03

    The Elf writes:

    "Top" is relative in this case. Obviously, to have the sort of "top" be literally the top meant in the question, the pencil will have to be balanced on its point--not very feasible except in zero-g. In reality, whatever part of the pencil is uppermost is per se the top. (The opposite side is, of course, the bottom.) So yes, the "right" answer is indeed 1/5.
    Of course, this ignores the fact that most wooden pencils are cut into hexagonal prisms, not pentagonal. And yes, I'm aware of special non-rolling triangular pencils, carpenter's pencils with two opposing wide, flat sides perpendicular to its two narrow opposing sides, round pencils, mechanical pencils with clips that might prevent rolling at all, and myriad other uncommon variations.

    Another objection: it is very difficult to roll a prismatic pencil. (That's why they ARE prismatic.) We should have to assume that to assure randomness, the pencil be dropped from a height, not rolled.

    All in all, I believe that whoever set the question in the first place thinks him/herself much cleverer that reality suggests!

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