A problem courtesy of Shakespeare

This note is about a powerful tool for solving problems, viz. calculation. Consider the following problem from Shakespeare’s The Merchant of Venice:

Portia has a gold casket and a silver casket and has placed a picture of herself in one of them. On the caskets she has written the following inscriptions:

Gold: The portrait is not here.
Silver: Exactly one of these inscriptions is true.

Portia explains to her suitor that each inscription may be true or false, but that she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions. If he can choose the casket with her portrait, she will marry him. The problem for the suitor is to use the inscriptions (although they may be either true or false) to determine which casket contains her portrait.

How can we solve this problem? Read more

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4 Responses to “A problem courtesy of Shakespeare”

  1. vlorbik Says:

    i’ve got this sneaky feeling that
    “exactly one of these propositions is true”
    isn’t a proposition at all …
    and a dead certainty that
    *i* can’t make any sense at all of
    “… she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions.”

    portia may be smarter than me …
    but i think she’s blowing smoke.

  2. Carnival of Mathematics #21: Bar-hopping at last « Secret Blogging Seminar Says:

    [...] for Mortals uses A problem courtesy of Shakespeare (which doesn’t match too well with my recollection of the Merchant of Venice, but let’s [...]

  3. Jonathan Vos Post Says:

    From Shakespeare’s The Merchant of Venice.

    PORTIA: The quality of mercy is not strain’d,

    It droppeth as the gentle rain from heaven
    Upon the place beneath: it is twice blest
    [i.e. blessed x 2];
    It blesseth him that gives and him that takes
    [i.e. + and -, or adjoint functors, or something like that]

    “The quality of mercy is not strained” through a sieve of Eratosthenes?

    Profit and loss analysis, with mathematical biotechnology focus:

    Fom Shakespeare’s Merchant of Venice, 1596. The insistence by Shylock of the payment of Antonio’s flesh is the central plot device of the play:

    SHYLOCK:
    The pound of flesh which I demand of him Is deerely bought, ’tis mine, and I will haue it.

    The figurative use of the phrase to refer to any lawful but nevertheless unreasonable recompense dates to the late 18th century.

  4. Denise Says:

    This is a good example of a problem where Guess-and-Check works more efficiently than the 4-page explanation at the link. The portrait either is or is not in the gold casket. If it is not, the inscription on the silver casket turns into one of those logical nonsense statements like “This statement is false,” which can be true if and only if it is not true.

    So the question becomes, do you trust Portia, or don’t you?

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